CCTV

#被数学选中的人 #数学 #纪录片

《被数学选中的人》第4集 Chosen By Mathematics EP4 普通人距离数学家有多遥远?抽象思维是与生俱来的吗?【CCTV纪录】

 

本期内容:数学之美,似乎只有少数人才能感受,但其实不管你是否是那个被数学选中的人,数学之美都在潜移默化地影响、改变、塑造着你。数学存在的意义,从来不是成为一件艺术品,而是作为一种人类智慧指引我们前行的方向。如果被数学选中的人是一个集合的话,它与人类这个集合应该是一样大的。

#Bèi shùxué xuǎnzhōng de rén#shùxué#jìlùpiàn bèi shùxué xuǎnzhōng de rén dì 4 jí Chosen By Mathematics EP4 pǔtōng rén jùlí shùxué jiā yǒu duō yáoyuǎn? Chōuxiàng sīwéi shì yǔ shēng jù lái de ma?[CCTV jìlù] běn qí nèiróng: Shùxué zhīměi, sìhū zhǐyǒu shǎoshù rén cáinéng gǎnshòu, dàn qíshí bùguǎn nǐ shìfǒu shì nàgè bèi shùxué xuǎnzhōng de rén, shùxué zhīměi dū zài qiányímòhuà dì yǐngxiǎng, gǎibiàn, sùzàozhe nǐ. Shùxué cúnzài de yìyì, cónglái bu shì chéngwéi yī jiàn yìshù pǐn, ér shì zuòwéi yī zhǒng rénlèi zhìhuì zhǐyǐn wǒmen qián xíng de fāngxiàng. Rúguǒ bèi shùxué xuǎnzhōng de rén shì yīgè jíhé dehuà, tā yǔ rénlèi zhège jíhé yīnggāi shì yīyàng dà de.

– #chosen by math #math #documentary

The Chosen By Mathematics Episode 4 Chosen By Mathematics EP4 How far are ordinary people from mathematicians? Is abstract thinking innate? 【CCTV record】

Contents of this issue: The beauty of mathematics seems to be felt by only a few people, but in fact, regardless of whether you are the one chosen by mathematics, the beauty of mathematics is subtly affecting, changing, and shaping you. The meaning of mathematics is never to be a work of art, but to guide us as a kind of human wisdom. If the people chosen by mathematics are a set, it should be as large as the set of humans.

 

第四集

抽象的巨人

Dì sì jí chōuxiàng de jùrén

– Episode 4 – abstract giant

 

我们尝试着为学习数学找到一些理由。比如数学直接决定着人类的宇宙观。Wǒmen chángshìzhe wéi xuéxí shùxué zhǎodào yīxiē lǐyóu. Bǐrú shǔ xué zhíjiē juédìngzhe rénlèi de yǔzhòuguān. – We try to find some reasons for studying mathematics. For example, mathematics directly determines the human view of the universe.

数学的发展深刻影响着我们的价值取向。Shùxué de fǎ zhǎn shēnkè yǐngxiǎngzhe wǒmen de jiàzhí qǔxiàng. – The development of mathematics has a profound impact on our value orientation.

数学教育对于个体的塑造 | 起着至关重要的作用。不过根据人的体性 | 我们更愿意 | 为自己学不好数学 | 找到一些说得过去的借口 | 比如数学确实很难 | 比如我们要承认 | 有的人天生不是学数学的科 | 而有的人生来 | 就是数学天赋携带者 | 他们才是被数学选中的人 | 真的是这样吗?Shùxué jiàoyù duìyú gètǐ de sùzào | qǐzhe zhì guān zhòngyào de zuòyòng. Bùguò gēnjù rén de tǐ xìng | wǒmen gèng yuànyì | wèi zìjǐ xué bù hǎo shùxué | zhǎodào yīxiē shuōdéguòqù de jièkǒu | bǐrú shǔ xué quèshí hěn nán | bǐrú wǒmen yào chéngrèn | yǒu de rén tiānshēng bùshì xué shùxué de kē | ér yǒu de rénshēng lái | jiùshì shùxué tiānfù xiédài zhě | tāmen cái shì bèi shùxué xuǎnzhōng de rén | zhēn de shì zhèyàng ma? – Mathematics education plays a vital role in shaping the individual | However, according to human nature | we prefer | to learn mathematics for ourselves | to find some plausible excuses | for example, mathematics is really difficult | for example, we have to admit | some people are not born to study mathematics | | They are the mathematical talent carriers | They are the ones chosen by mathematics | Is that really true?

数学真的很难。数学当然是难的。对于它我一直是景仰的。难是数学的一个特点 | 甚至可以说是它的一个性质。Shùxué zhēn de hěn nán. Shùxué dāngrán shì nán de. Duìyú tā wǒ yīzhí shì jǐngyǎng de. Nán shì shùxué de yīgè tèdiǎn | shènzhì kěyǐ shuō shì tā de yīgè xìngzhì. – Math is really hard. Math is of course difficult. I have always admired it. Difficulty is a feature of mathematics | it can even be said to be a property of it.

学数学不应该说它难 | 可能研究数学会难 | 研究数学的时候他是比较孤独的。Xué shùxué bù yìng gāi shuō tā nán | kěnéng yánjiū shùxué huì nán | yánjiū shùxué de shíhòu tā shì bǐjiào gūdú de. – It should not be said that it is difficult to study mathematics | Maybe studying mathematics will be difficult | He is relatively lonely when studying mathematics.

不在难易吧,就看你喜不喜欢 | 喜欢做的事越难越有意思 | 不喜欢的话再简单也不想去做 | 是吧?Bùzài nán yì ba, jiù kàn nǐ xǐ bù xǐhuān | xǐhuān zuò de shì yuè nán yuè yǒuyìsi | bù xǐhuān dehuà zài jiǎndān yě bùxiǎng qù zuò | shì ba? – It’s not difficult or easy, it depends on whether you like it or not | The harder you like to do, the more interesting it is | If you don’t like it, no matter how easy it is, you don’t want to do it | Right?

那么其实说句实在说 | 我们从小学到高中毕业 | 我们对于那个复杂的计算 | 也是很畏惧的 | 那个复杂的计算 | 也是造成我们困难的因素之一。Nàme qíshí shuō jù shízài shuō | wǒmen cóng xiǎoxué dào gāozhōng bìyè | wǒmen duìyú nàgè fùzá de jìsuàn | yěshì hěn wèijù de | nàgè fùzá de jìsuàn | yěshì zàochéng wǒmen kùnnán de yīnsù zhī yī. – Well, to tell the truth | We graduated from elementary school to high school | We are also very afraid of that complex calculation | That complex calculation | is also one of the factors that cause our difficulties.

有困难有挑战 | 才让我们这些人如痴如迷,对吧?| 就好像一个男生要去追 | 班上最漂亮的女生 | 如果那么容易就追到 | 那么容易可能吗? | 难的东西做起来才会有意思。Yǒu kùn nàn yǒu tiǎozhàn | cái ràng wǒmen zhèxiē rén rú chī rú mí, duì ba?| Jiù hǎoxiàng yīgè nánshēng yào qù zhuī | bān shàng zuì piàoliang de nǚshēng | rúguǒ nàme róngyì jiù zhuī dào | nàme róngyì kěnéng ma? | Nán de dōngxī zuò qǐlái cái huì yǒuyìsi. – Difficulties and challenges | That’s what keeps us people obsessed, right? | It’s like a boy is going to chase | The most beautiful girl in the class | If it’s that easy to catch up | Is it that easy? | Difficult things are fun to do.

尽管对于难得定义和层级 | 大家会有各自的理解和界定 | 但能听到数学家们 | 发出同样的感叹 | 实在是一件值得欣慰的事 | 这足以说明数学确实很难。Jǐnguǎn duìyú nándé dìngyì hé céngjí | dàjiā huì yǒu gèzì de lǐjiě hé jièdìng | dàn néng tīng dào shùxué jiāmen | fāchū tóngyàng de gǎntàn | shízài shì yī jiàn zhídé xīnwèi de shì | zhè zúyǐ shuōmíng shùxué quèshí hěn nán. – Although everyone has their own understandings and definitions for rare definitions and levels | but it is really gratifying to hear mathematicians | exclaiming the same | This is enough to show that mathematics is indeed difficult.

那么它到底难在哪里呢?数学很难是因为数学它的最主要的处理的对象是非常抽象的数量关系。Nàme tā dàodǐ nán zài nǎlǐ ne? Shùxué hěn nán shì yīn wéi shùxué tā de zuì zhǔyào de chǔlǐ de duìxiàng shì fēicháng chōuxiàng de shùliàng guānxì. – So what’s so difficult about it? Mathematics is difficult because mathematics mostly deals with very abstract quantitative relationships.

实际上抽象性这和难应该说是占据绝对的第一位的。Shíjì shang chōuxiàng xìng zhè hé nán yīnggāi shuō shì zhànjù juéduì de dì yī wèi de. – In fact, abstraction and difficulty should be said to occupy the absolute first place.

比方说我手上这个是什么?大家一定会说 这就是一 | 然后一是什么 | 其实大家从来都没见过 | 因为一就是一个抽象的概念。Bǐfāng shuō wǒ shǒu shàng zhège shì shénme? Dàjiā yì dìng huì shuō zhè jiùshì | ránhòu yī shì shénme | qíshí dàjiā cónglái dōu méi jiànguò | yīn wéi yī jiùshì yīgè chōuxiàng de gàiniàn. – Like what is this in my hand? Everyone must say „This is one” | Then what is one | Actually, no one has ever seen it | Because one is an abstract concept.

因为受到感官的制约 | 我们看到的世界 | 并不是完全真实的 | 所以如果想 | 离真正的机理和本质更近一点 | 数学抽象或许是最有效的途径。Yīnwèi shòudào gǎnguān de zhìyuē | wǒmen kàn dào de shìjiè | bìng bùshì wánquán zhēnshí de | suǒyǐ rúguǒ xiǎng | lí zhēnzhèng de jīlǐ hé běnzhí gèng jìn yīdiǎn | shùxué chōuxiàng huòxǔ shì zuì yǒuxiào de tújìng. – Because of the constraints of the senses | the world we see | is not completely real | so if you want to | get closer to the real mechanism and essence | mathematical abstraction may be the most effective way.

我们去掉所有感性的东西之后,比如轻重,大小, 软硬,冷热 等等,其背后的各和结构,才有可能显现出来。Wǒmen qùdiào suǒyǒu gǎnxìng de dōngxī zhīhòu, bǐrú qīngzhòng, dàxiǎo, ruǎn yìng, lěng rè děng děng, qí bèihòu de gè hé jiégòu, cái yǒu kěnéng xiǎnxiàn chūlái. – After we remove all perceptual things, such as weight, size, softness, hardness, hot and cold, etc., the various and structures behind it can be revealed.

抽象之后你会发现另外一个世界。在这个世界里事物被重新定义。Chōuxiàng zhīhòu nǐ huì fāxiàn lìngwài yīgè shìjiè. Zài zhège shìjiè lǐ shìwù bèi chóngxīn dìngyì. – After abstraction you will find another world. In this world things are redefined.

当我们带着这些关系和结构 | 再次回到现实世界 | 它可以创造出很多新的东西 | 可以追溯过去 | 应对现在 | 也可以预测未来。Dāng wǒmen dàizhe zhèxiē guānxì hé jiégòu | zàicì huí dào xiànshí shìjiè | tā kěyǐ chuàngzào chū hěnduō xīn de dōngxī | kěyǐ zhuīsù guòqù | yìngduì xiànzài | yě kěyǐ yùcè wèilái. – When we take these relationships and structures | back to the real world again | it can create a lot of new things | can go back to the past | deal with the present | can also predict the future.

传说伟大的数学家笛卡尔 | 在梦中获得了坐标系的灵感 | 从而找到了用代数方法 | 解释几何问题的桥梁 | 这便是用一种抽象 | 去表达另一种抽象 | 坐标系的概念其实是很抽象的 | 但由于我们受到过 | 系统的数学教育 | 这个抽象的概念 | 反而在头脑中变得清晰明了。Chuánshuō wěidà de shùxué jiā dí kǎ’ěr | zài mèng zhōng huòdéle zuòbiāo xì de línggǎn | cóng’ér zhǎodàole yòng dàishù fāngfǎ | jiěshì jǐhé wèntí de qiáoliáng | zhè biàn shì yòng yī zhǒng chōuxiàng | qù biǎodá lìng yī zhǒng chōuxiàng | zuòbiāo xì de gàiniàn qíshí shì hěn chōuxiàng de | dàn yóuyú wǒmen shòudàoguò | xìtǒng de shùxué jiàoyù | zhège chōuxiàng de gàiniàn | fǎn’ér zài tóunǎo zhōng biàn dé qīngxī míngliǎo. – Legend has it that the great mathematician Descartes | got the inspiration of the coordinate system in a dream | and thus found a bridge to explain the geometric problem with algebra | This is to use an abstract | to express another abstract | the concept of a coordinate system In fact, it is very abstract | but because we have received | systematic mathematics education | this abstract concept | has become clear in our minds.

数学抽象有个特征是多级抽象 | 就是在已有抽象的基础上 | 进一步抽象 | 那么这个就离我们的 | 现实直观的东西越来越远。Shùxué chōuxiàng yǒu gè tèzhēng shì duō jí chōuxiàng | jiùshì zài yǐ yǒu chōuxiàng de jīchǔ shàng | jìnyībù chōuxiàng | nàme zhège jiù lí wǒmen de | xiànshí zhíguān de dōngxī yuè lái yuè yuǎn. – One of the characteristics of mathematical abstraction is multi-level abstraction | that is, based on the existing abstraction | further abstraction | Then this is farther and farther away from our | realistic and intuitive things.

它可以通过一来构造二来构造三 | 来构造一百 | 然后甚至构造究大 | 然后这个只是基于 | 某一种抽象构造更加的抽象 | 所以在数学世界里面 | 其实没有什么是最抽象 | 只有更抽象。Tā kěyǐ tōngguò yī lái gòuzào èr lái gòuzào sān | lái gòuzào yībǎi | ránhòu shènzhì gòuzào jiū dà | ránhòu zhège zhǐshì jīyú | mǒu yī zhǒng chōuxiàng gòuzào gèngjiā de chōuxiàng | suǒyǐ zài shùxué shìjiè lǐmiàn | qíshí méiyǒu shé me shì zuì chōuxiàng | zhǐyǒu gèng chōuxiàng. – It can use one to construct two to construct three | to construct one hundred | and then even to construct the big| more abstract.

人类的思考方式受语言支配 | 数学可以被看作是一种 | 特殊的语言 | 它可以帮助我们去刻画那些 | 最基本的原理种最普遍的规律 | 全世界大约有六千种语言 | 却只有一种数学 | 它是抽象的符号化的 | 以至于根本找不到实物 | 但却与物理世界 | 产生了惊人的吻合 | 这就是数学的威力 | 数学抽象让我们有机会 | 从里向外看问题 | 从高处向下看问题 | 去除掉所有的外部于扰 | 向本质靠近。Rénlèi de sīkǎo fāngshì shòu yǔyán zhīpèi | shùxué kěyǐ bèi kàn zuò shì yī zhǒng | tèshū de yǔyán | tā kěyǐ bāngzhù wǒmen qù kèhuà nàxiē | zuì jīběn de yuánlǐ zhǒng zuì pǔbiàn de guīlǜ | quán shìjiè dàyuē yǒu liùqiān zhǒng yǔyán | què zhǐyǒu yī zhǒng shùxué | tā shì chōuxiàng de fúhào huà de | yǐ zhìyú gēnběn zhǎo bù dào shíwù | dàn què yǔ wùlǐ shìjiè | chǎnshēngle jīngrén de wěnhé | zhè jiùshì shùxué de wēilì | shùxué chōuxiàng ràng wǒmen yǒu jīhuì | cóng lǐ xiàng wài kàn wèntí | cóng gāo chù xiàng xià kàn wèntí | qùchú diào suǒyǒu de wàibù yú rǎo | xiàng běnzhí kàojìn. – The way humans think is governed by language|Mathematics can be seen as a|special language|it can help us to describe those|most basic principles and the most general laws|There are about 6000 languages in the world| A kind of mathematics|it is abstract and symbolic|so that you can’t find the real thing|but it fits with the physical world| Problem | Looking down on the problem from above | Remove all external disturbances | Approach to the essence.

如同大航海时代 | 远航者依靠手中的测量工具 | 在茫茫大海中寻找方向 | 发现新的物种 | 新的规律 | 数学家们用前人创造的数学理论 | 在抽象世界里 | 不断深素着真实世界存在的意义。Rútóng dà hánghǎi shídài | yuǎnháng zhě yīkào shǒuzhōng de cèliáng gōngjù | zài mángmáng dàhǎi zhōng xúnzhǎo fāngxiàng | fāxiàn xīn de wùzhǒng | xīn de guīlǜ | shùxué jiāmen yòng qián rén chuàngzào de shùxué lǐlùn | zài chōuxiàng shìjiè lǐ | bùduàn shēn sùzhe zhēnshí shìjiè cúnzài de yìyì. – Just like the age of voyages | Voyagers rely on measuring tools in their hands | Looking for directions in the vast ocean | Discovering new species | New laws | Mathematicians use the mathematical theories created by predecessors | In the abstract world | the meaning of the world’s existence.

在看到数学新人大陆的地平线之前 | 数学家们提出假定和猜想 | 为今后的航程 | 确立一条模糊的航线 | 这些假定和猜想 | 便成为了难题中的难题 | 如果后人可以证明其正确 | 那么数学奖被开拓出 | 一片崭新的领域 | 如果被证明错误 | 那么人们之前 | 在这个假定基础上做出的很多工作 | 便失去了根据。Zài kàn dào shùxué xīnrén dàlù dì dìpíngxiàn zhīqián | shùxué jiāmen tíchū jiǎdìng hé cāixiǎng | wéi jīnhòu de hángchéng | quèlì yītiáo móhú de hángxiàn | zhèxiē jiǎdìng hé cāixiǎng | biàn chéngwéile nántí zhōng de nántí | rúguǒ hòu rén kěyǐ zhèngmíng qí zhèngquè | nàme shùxué jiǎng bèi kāità chū | yīpiàn zhǎnxīn de lǐngyù | rúguǒ bèi zhèngmíng cuòwù | nàme rénmen zhīqián | zài zhège jiǎdìng jīchǔ shàng zuò chū de hěnduō gōngzuò | biàn shīqùle gēnjù. – Before seeing the horizon of the new continent of mathematics | Mathematicians put forward assumptions and conjectures | Establish a vague route for future voyages | These assumptions and conjectures | become the difficult problems in the puzzle| If future generations can prove it correct| Then the mathematics prize is opened up | a whole new field | if proven wrong | then a lot of the previous work | based on this assumption | has no basis.

在本世纪初 | 美国克雷数学研究所选定了七个 千年大奖问题 | 每个问题悬赏一百万美元 | 这七个 千年大奖问题 是 | NP 完全问题 霍奇猜想 | 庞加莱猜想 黎曼假设杨-米尔斯理论 | 纳维尔-斯托克斯方程 | BSD 猜想Zài běn shìjì chū | měiguó kè léi shùxué yánjiū suǒ xuǎn dìngle qī gè qiānnián dàjiǎng wèntí” | měi gè wèntí xuánshǎng yībǎi wàn měiyuán | zhè qī gè qiānnián dàjiǎng wèntí” shì | NP wánquán wèntí” huò qí cāixiǎng | páng jiā lái cāixiǎng lí màn jiǎshè” | yáng-mǐ’ěr sī lǐlùn | nà wéi’ěr-sī tuō kè sī fāngchéng | hé BSD cāixiǎng. – At the beginning of this century | The Clay Mathematical Institute of the United States selected seven „Millennium Prize problems” | Each question offered a reward of one million dollars | These seven „Millennium Prize problems” are | „NP complete problems” „Hodge conjecture” ” | „Poincaré Conjecture” „Riemann Hypothesis” | „Young-Mills Theory” | „Navier-Stokes Equations” | and „BSD Conjecture”.

这大概是全世界最难挣到的一笔巨款 | 这些难题科学如此发达的今天 | 仍热令那些最聪明的大脑 | 感到束手无策 | 哪怕只在证明的道路上 | 推进一步 | 便足以青史留名。Zhè dàgài shì quán shìjiè zuì nán zhēng dào de yī bǐ jù kuǎn | zhèxiē nántí kēxué rúcǐ fādá de jīntiān | réng rè lìng nàxiē zuì cōngmíng de dànǎo | gǎndào shùshǒuwúcè | nǎpà zhǐ zài zhèngmíng de dàolù shàng | tuī jìnyībù | biàn zúyǐ qīngshǐ liú míng. – This is probably the hardest huge sum of money in the world | these difficult problems are so advanced in science today | still hot to the brightest brain | feel helpless | even if only on the road of proof | a step forward | is enough to stay in history name.

截正到今天 | 这七个难题中 | 只有 庞加莱猜想 | 被俄罗斯数学家佩雷尔曼成功证明 | 这位淡泊名利的数学天才 | 在震惊了世界之后 | 却拒绝了 数学界的诺见尔奖 | 菲尔茨奖的荣誉 | 以及一百万美元的奖金 | 人间蒸发般地隐居了。Jié zhèng dào jīntiān | zhè qī gè nántí zhōng | zhǐyǒu páng jiā lái cāixiǎng | bèi èluósī shùxué jiā pèi léi ěr màn chénggōng zhèngmíng | zhè wèi dànbó mínglì de shùxué tiāncái | zài zhènjīngle shìjiè zhīhòu | què jùjuéle shùxué jiè de nuò jiàn ěr jiǎng | fēi ěr cí jiǎng de róngyù | yǐjí yībǎi wàn měiyuán de jiǎngjīn | rénjiān zhēngfā bān de yǐnjūle. – As of today | Of these seven problems | Only „Poincaré conjecture” | Successfully proved by Russian mathematician Perelman | This indifferent mathematical genius | After shocking the world | The Nobel Prize” | Fields Medal honors | and a million dollar prize | evaporated into recluse.

七个难题著名的 | 就算是 黎曼假设 | 也叫 黎曼猜想 了。Qī gè nántí zhùmíng de | jiùsuàn shì lí màn jiǎshè” | yě jiào lí màn cāixiǎngle. – The famous seven problems | Even the „Riemann hypothesis” | is also called the „Riemann hypothesis”.

黎曼是十九世纪德国的数学天才 | 他开创的黎曼几何 | 为后来爱因斯坦 | 提出广义相对论提供了数学工具。Lí màn shì shíjiǔ shìjì déguó de shùxué tiāncái | tā kāichuàng dí lí màn jǐhé | wèi hòulái ài yīn sītǎn | tíchū guǎngyì xiāngduìlùn tígōngle shùxué gōngjù. – Riemann was a German mathematical genius in the 19th century | Riemannian geometry he created | provided mathematical tools for Einstein | to propose the general theory of relativity.

黎曼猜想跟素数有关 | 之前我们提到的 哥德吧赫猜想 | 也是关于素数的。Lí màn cāixiǎng gēn sùshù yǒuguān | zhīqián wǒmen tí dào de gē dé ba hè cāixiǎng | yěshì guānyú sù shǔ de. – The Riemann conjecture is related to prime numbers | the „Godbach conjecture” we mentioned earlier | is also about prime numbers.

为什么数学家对素数这么情有独钟呢?

所谓素数就是除了一和自身外 | 不能被其它整数整除的数字 | 这里面当然就排除了 | 除二之外的偶数 | 奇数中 | 三,五,七 都是素数 | 而九由于可以被三整除 | 就不是素数了 | 由此我们可以一直寻找不去。Wèishéme shùxué jiā duì sùshù zhème qíng yǒu dú zhōng ne? Suǒwèi sùshù jiùshì chúle yī hè zìshēn wài | bùnéng bèi qítā zhěngshù zhěngchú de shùzì | zhè lǐmiàn dāngrán jiù páichúle | chú èr zhī wài de ǒushù | jīshù zhōng | sān, wǔ, qī dōu shì sùshù | ér jiǔ yóuyú kěyǐ bèi sān zhěngchú | jiù bùshì sùshùle | yóu cǐ wǒmen kěyǐ yīzhí xúnzhǎo bù qù. – Why do mathematicians have such a soft spot for prime numbers?

The so-called prime number is a number that is not divisible by other integers except one and itself | of course it excludes | even numbers except two | odd numbers | three, five, seven are prime numbers | and nine can be divided by three | is not a prime number | From this we can keep looking for it.

当我们找到数量足够大的素数后却发现 | 素数的排布是毫无规律的 | 这引起了自古以来 | 数学家们的注意。Dāng wǒmen zhǎodào shùliàng zúgòu dà de sùshù hòu què fāxiàn | sù shǔ de pái bù shì háo wú guīlǜ de | zhè yǐnqǐle zìgǔ yǐlái | shùxué jiāmen de zhùyì. – When we find a large enough number of prime numbers, we find that | the arrangement of prime numbers is irregular | This has attracted the attention of mathematicians since ancient times.

黎曼提出了一个函数 | 当这个函数取值为零的 | 对应的一系列特殊点 | 对素数分布的规律 | 有着决定性的影响 | 这个函数就叫做黎曼 ζ 函数 | 一系列特殊的点 | 就叫做非平凡零点 | 黎曼推断这些非平凡零点都位于一条直线上。Lí màn tíchūle yīgè hánshù | dāng zhège hánshù qǔ zhí wéi líng de | duìyìng de yī xìliè tèshū diǎn | duì sùshù fēnbù de guīlǜ | yǒuzhe juédìngxìng de yǐngxiǎng | zhège hánshù jiù jiàozuò lí màn z hánshù | yī xìliè tèshū de diǎn | jiù jiàozuò fēi píngfán língdiǎn | lí màn tuīduàn zhèxiē fēi píngfán língdiǎn dōu wèiyú yītiáo zhíxiàn shàng. – Riemann proposed a function | when this function takes a value of zero | corresponding to a series of special points | has a decisive influence on the law of prime number distribution | this function is called Riemann zeta function | a series of special points | called non-trivial zeros | Riemann inferred that these non-trivial zeros all lie on a straight line.

对普通人来说 | 这些令人一头雾水的理论 | 如同天书一般 | 但对数学家来说 | 揭开数字之谜的诱惑 | 成为之后一百五十年间 | 聪明大脑们殚精竭虑 | 一点点向证明 黎曼猜想 | 挪动的精神支柱。Duì pǔtōng rén lái shuō | zhèxiē lìng rén yītóu wù shuǐ de lǐlùn | rútóng tiānshū yībān | dàn duì shùxué jiā lái shuō | jiē kāi shùzì zhī mí de yòuhuò | chéngwéi zhīhòu yībǎi wǔshí niánjiān | cōngmíng dànǎomen dānjīngjiélǜ | yī diǎndiǎn xiàng zhèngmíng lí màn cāixiǎng | nuódòng de jīngshén zhīzhù. – To ordinary people| these confusing theories| like a book from the sky| but to mathematicians| the temptation to solve the mystery of numbers| for one hundred and fifty years after becoming| Prove the „Riemann Conjecture” | The spiritual pillar of movement.

首先一八九六年 | 法国数学家哈达玛 | 和比利时数学家普桑 | 证明了非平凡零点 | 存在于一个区域的内部 | 而不在区域的边界 | 一九一四年丹麦数学家玻尔 | 和德国数学家兰道 | 进一步证明 | 这些非平凡零点倾向于 | 紧密团结在临界线的周围 | 这离 黎曼猜想 的范围 | 又缩小了一步。Shǒuxiān yībājiǔliù nián | fàguó shùxué jiā hādá mǎ | hé bǐlìshí shùxué jiā pǔ sāng | zhèngmíngliǎo fēi píngfán língdiǎn | cúnzài yú yīgè qūyù de nèibù | ér bùzài qūyù de biānjiè | yījiǔyīsì nián dānmài shùxué jiā bō ěr | hé déguó shùxué jiā lán dào | jìnyībù zhèngmíng | zhèxiē fēi píngfán língdiǎn qīngxiàng yú | jǐnmì tuánjié zài línjiè xiàn de zhōuwéi | zhè lí lí màn cāixiǎng de fànwéi | yòu suōxiǎole yībù. – First, 1896 | French mathematician Hadamard | and Belgian mathematician Poussin | proved that non-trivial zeros | exist in the interior of a region| And German mathematician Landau | Further proof | These non-trivial zeros tend to | „closely pack around the critical line” | This is one step closer to the „Riemann conjecture”.

同一年 | 英国数学家哈代终于证明 | 有无究多个非平凡零点 | 在这条临界线上 | 但这并不意味着 | 黎曼猜想 被证明了 | 因为尽管称为无究多个 | 但这并不能认为是 | 全部的非平凡零点。Tóngyī nián | yīngguó shùxué jiā hādài zhōngyú zhèngmíng | yǒu wú jiū duō gè fēi píngfán língdiǎn | zài zhè tiáo línjiè xiàn shàng | dàn zhè bìng bù yìwèizhe | lí màn cāixiǎng bèi zhèngmíngliǎo | yīnwèi jǐnguǎn chēng wéi wú jiū duō gè | dàn zhè bìng bùnéng rènwéi shì | quánbù de fēi píngfán língdiǎn. – In the same year | British mathematician Hardy finally proved | whether there are many non-trivial zeros | on this critical line | but this does not mean | „Riemann conjecture” has been proved | | But this cannot be considered to be | all non-trivial zeros.

哈代进一步研究之后沮丧的发现 | 位于临界线上的 | 无究多个非平凡零点 | 跟全部非平凡零点的比例 | 居然近似等于百分之零。Hādài jìnyībù yánjiū zhīhòu jǔsàng de fǎ xiàn | wèiyú línjiè xiàn shàng de | wú jiū duō gè fēi píngfán língdiǎn | gēn quánbù fēi píngfán língdiǎn de bǐlì | jūrán jìnsì děngyú bǎi fēn zhī líng. – Hardy’s dismaying discovery after further research | on the critical line | regardless of the ratio of multiple non-trivial zeros | to all non-trivial zeros | is approximately equal to zero percent.

二十一年后 | 令人振奋的消息传来 | 挪威数学家塞尔伯格 | 在二战的硝烟中 | 孤独而坚韧地工作着 | 他证明上面的那个比例不是百分之零 | 而是大于零 | 是的 | 黎曼猜想 的证明就是这样 | 一小步一小步地推进着。Èrshíyī nián hòu | lìng rén zhènfèn de xiāoxī chuán lái | nuówēi shùxué jiā sài ěr bó gé | zài èrzhàn de xiāoyān zhòng | gūdú ér jiānrèn dì gōngzuòzhe | tā zhèngmíng shàngmiàn dì nàgè bǐlì bùshì bǎi fēn zhī líng | ér shì dàyú líng | shì de | lí màn cāixiǎng de zhèngmíng jiùshì zhèyàng | yī xiǎo bù yī xiǎo bù de tuījìnzhe. – Twenty-one years later | Exciting news comes | Norwegian mathematician Selberg | In the smoke of World War II | Working alone and tenaciously | He proves that the above ratio is not zero percent | Zero | Yes | The proof of „Riemann’s conjecture” is just this | small step by step.

一九七四年美国数学家列文森证明至小有百分之三十四的零点在临界线上。Yījiǔqīsì nián měiguó shùxué jiā liè wén sēn zhèngmíng zhì xiǎo yǒu bǎi fēn zhī sānshísì de língdiǎn zài línjiè xiàn shàng. – In 1974, the American mathematician Levinson proved that 34% of the zeros are on the critical line.

 中国数学家楼世拓与姚琦艰难地把这个百分比推进到百分之三十五。Zhōngguó shùxué jiā lóu shì tà yǔ yáo qí jiānnán de bǎ zhège bǎifēnbǐ tuījìn dào bǎi fēn zhī sānshíwǔ. – Chinese mathematicians Lou Shituo and Yao Qi struggled to push the percentage to 35 percent.

一九八九年美国数学家康瑞再进一步 | 百分比被提高到了百分之四十 | 这是到日前为止 | 关于 黎曼猜想 的最强论证 | 除了论证非平凡零点 | 在临界线上的比例 | 人们也在关注 | 具体这些零点的数量 | 但是哪怕只证明一个零点 | 也需要令人望而生畏的大计算。Yījiǔbājiǔ nián měiguó shùxué jiākāng ruì zài jìnyībù | bǎifēnbǐ bèi tígāo dào liǎo bǎi fēn zhī sìshí | zhè shì dào rìqián wéizhǐ | guānyú lí màn cāixiǎng de zuì qiáng lùnzhèng | chúle lùnzhèng fēi píngfán língdiǎn | zài línjiè xiàn shàng de bǐlì | rénmen yě zài guānzhù | jùtǐ zhèxiē língdiǎn de shùliàng | dànshì nǎpà zhǐ zhèngmíng yīgè língdiǎn | yě xūyào lìng rén wàng’érshēngwèi de dà jìsuàn. – In 1989, American mathematician Conroy went further | The percentage was raised to 40% | This is the strongest argument for the „Riemann conjecture” so far | Except for the non-trivial zero point of the argument | On the critical line Proportion|People are also concerned|specifying the number of these zeros| but proving even one zero| requires dauntingly large calculations.

一千九百零三年丹麦数学家格兰姆计算出了十五个零点的数值 | 它们都准确地位于 | 黎曼预言的临界线上 | 到一千九百二十五年 | 数学家们计算出了一百三十八个零点。Yīqiān jiǔbǎi líng sān nián dānmài shùxué jiā gé lán mǔ jìsuàn chūle shíwǔ gè língdiǎn de shùzhí | tāmen dōu zhǔnquè dì wèiyú | lí màn yùyán de línjiè xiàn shàng | dào yīqiān jiǔbǎi èrshíwǔ nián | shùxué jiāmen jìsuàn chūle yībǎi sānshíbā gè língdiǎn. – In 1903 the Danish mathematician Graham calculated the value of fifteen zeros | they all lie exactly on | the critical line predicted by Riemann | by 1925 | mathematicians One hundred and thirty-eight zeros were calculated.

一千九百三年  德国数学家西格尔 | 从黎曼残存的手稿中 | 发现了黎曼早就创造出的一种 | 比猜想推出七十年后 | 还要高超得多的 | 计算零点的公式 | 在这个公式的推动下 | 很快零点的数量 | 就被计算了一千个 | 计算机技术的发展 | 使得人的计算能力越发强大 | 零点的数量得到了开喷式的增长 | 从一千个到二万五千个 | 再到三百五十万个 | 一千九百七十九年  变成了八千一百万个 | 接着是二亿个三亿个。Yīqiān jiǔbǎi sān nián déguó shùxué jiā xī gé ěr | cóng lí màn cáncún de shǒugǎo zhōng | fāxiànle lí màn zǎo jiù chuàngzào chū de yī zhǒng | bǐ cāixiǎng tuīchū qīshí nián hòu | hái yào gāochāo dé duō de | jìsuàn língdiǎn de gōngshì | zài zhège gōngshì de tuīdòng xià | hěn kuài língdiǎn de shùliàng | jiù bèi jìsuànle yīqiān gè | jìsuànjī jìshù de fǎ zhǎn | shǐdé rén de jìsuàn nénglì yuèfā qiángdà | língdiǎn de shù liáng dédàole kāi pēn shì de zēngzhǎng | cóng yīqiān gè dào èr wàn wǔqiān gè | zài dào sānbǎi wǔshí wàn gè | yīqiān jiǔbǎi qīshíjiǔ nián biàn chéngle bāqiān yībǎi wàn gè | jiēzhe shì èr yì gè sān yì gè. – In 1913, German mathematician Siegel | From Riemann’s surviving manuscripts | found a kind of | created by Riemann long ago | seventy years after the conjecture was launched | much more advanced | calculation of zero The formula of | Driven by this formula | Soon the number of zeros| was counted by a thousand | The development of computer technology | made people’s computing power more and more powerful | The number of zeros has been increasing | One thousand to twenty-five thousand | three and a half million | eighty-one million in 1979 | followed by two hundred million three hundred million.

 这十万亿个非平凡零点也都在临界线之上。Zhè shí wàn yì gè fēi píngfán língdiǎn yě dū zài línjiè xiàn zhī shàng. – These ten trillion non-trivial zeros are also above the critical line.

然面再多数量的零点 | 被计算出符合规律 | 也不能证明 黎曼猜想 是完全正确的 | 数学猜想之所以被认为 | 是这个世界上最难的问题 | 就在于猜想体身 | 便是对抽象的规律 | 用抽象的理念进行假定 | 而数学家们又需要更抽象的方法 | 去解释这些抽象的概念 | 全人类面对数学时都可以慨叹 | 数学,你太难了。Rán miàn zài duō shùliàng de língdiǎn | bèi jìsuàn chū fúhé guīlǜ | yě bùnéng zhèngmíng lí màn cāixiǎng shì wánquán zhèngquè de | shùxué cāixiǎng zhī suǒyǐ bèi rènwéi | shì zhège shìjiè shàng zuì nán de wèntí | jiù zàiyú cāixiǎng tǐ shēn | biàn shì duì chōuxiàng de guīlǜ | yòng chōuxiàng de lǐniàn jìnxíng jiǎdìng | ér shùxué jiāmen yòu xūyào gèng chōuxiàng de fāngfǎ | qù jiěshì zhèxiē chōuxiàng de gàiniàn | quán rénlèi miàn duì shùxué shí dōu kěyǐ kǎitàn | shùxué, nǐ tài nánle. – However, no matter how many zero points | are calculated to be in line with the law | it cannot prove that the „Riemann conjecture” is completely correct | the reason why mathematical conjectures are considered | is the most difficult problem in the world | lies in guessing the body | It is the abstract laws | Assumptions with abstract ideas | And mathematicians need more abstract methods | To explain these abstract concepts | All human beings can sigh when faced with mathematics | Mathematics, you are too difficult.

难绝对是我们 | 学不好数学的理由之一 | 但我们又不得不面对这个 | 注定陪伴我们 | 整个学生时期的抽象巨人 | 我们又该以何种心态面对它呢?Nán juéduì shì wǒmen | xué bù hǎo shùxué de lǐyóu zhī yī | dàn wǒmen yòu bùdé bù miàn duì zhège | zhùdìng péibàn wǒmen | zhěnggè xuéshēng shíqí de chōuxiàng jùrén | wǒmen yòu gāi yǐ hé zhǒng xīntài miàn duì tā ne? – Difficulty is definitely one of the reasons why we | do not learn mathematics well | but we have to face this | destined to accompany us | the abstract giant of the whole student period | what kind of attitude should we face it?

怎么讲数学选我挺对的 | 因为数学在后天武装我之前 | 我似乎就具备了一定的 | 数学家应该有的思维方式 | 就是抓住规律 | 你学数学你要抓住它的规律 | 然后你很快就能上道。Zěnme jiǎng shùxué xuǎn wǒ tǐng duì de | yīn wéi shùxué zài hòutiān wǔzhuāng wǒ zhīqián | wǒ sìhū jiù jùbèile yīdìng de | shùxué jiā yīnggāi yǒu de sīwéi fāngshì | jiùshì zhuā zhù guīlǜ | nǐ xué shùxué nǐ yào zhuā zhù tā de guīlǜ | ránhòu nǐ hěn kuài jiù néng shàng dào. – How to choose me in mathematics | Because mathematics will arm me before the day after tomorrow | I seem to have a certain way of thinking | The way of thinking that a mathematician should have | is to grasp the law | You’ll be on your way soon.

一般的智力跟数学的好坏关系有但不是那么强 | 不是绝对的决定关系 | 甚至还可以说是比较弱的关系 | 但是有一个因素 | 跟数学的成绩好坏是比较稳定的 | 就是说发挥着比较大的决定作用 | 这个因素就是人的空间想象能力。Yībān de zhìlì gēn shùxué de hǎo huài guānxì yǒu dàn bùshì nàme qiáng | bùshì juéduì de juédìng guānxì | shènzhì hái kěyǐ shuō shì bǐjiào ruò de guānxì | dànshì yǒu yīgè yīnsù | gēn shùxué de chéngjī hǎo huài shì bǐjiào wěndìng de | jiùshì shuō fāhuīzhe bǐjiào dà de juédìng zuòyòng | zhège yīnsù jiùshì rén de kōngjiān xiǎngxiàng nénglì. – The general intelligence has a relationship with mathematics, but it is not so strong | It is not an absolute decisive relationship | It can even be said to be a relatively weak relationship | But there is a factor | It is relatively stable with the performance of mathematics | has a relatively large decisive role | This factor is the ability of people’s spatial imagination.

因为你要解决这些抽象的数量关系。Yīnwèi nǐ yào jiějué zhèxiē chōuxiàng de shùliàng guānxì. – Because you have to solve these abstract quantitative relationships.

心定要把抽象的数量关系 | 转换为一个空间结构 | 是关于空间结构的 | 哪怕阿拉伯数字 一二三四五六七八九 | 你看我刚才是按照顺序出来的 | 其实在你大脑里面的排列 | 就是一个空间结构 | 什么意思呢?就是阿拉伯数字的一二三 | 这种小数字 | 对于中国人而言 | 他是放在左边 | 七八九是放在右边 | 当然您现在是看不见 | 你可以想象出来 | 这就是一个空间结构。Xīn dìng yào bǎ chōuxiàng de shùliàng guānxì | zhuǎnhuàn wéi yīgè kōngjiān jiégòu | shì guānyú kōngjiān jiégòu de | nǎpà ālābó shùzì yī’èrsānsìwǔliùqībājiǔ | nǐ kàn wǒ gāngcái shì ànzhào shùnxù chūlái de | qíshí zài nǐ dànǎo lǐmiàn de páiliè | jiùshì yīgè kōngjiān jiégòu | shénme yìsi ne? Jiùshì ālābó shùzì de yī’èrsān | zhè zhǒng xiǎo shùzì | duìyú zhōngguó rén ér yán | tā shì fàng zài zuǒbiān | qībājiǔ shì fàng zài yòubiān | dāngrán nín xiànzài shì kàn bùjiàn | nǐ kěyǐ xiǎngxiàng chūlái | zhè jiùshì yīgè kōngjiān jiégòu. – The heart is determined to convert the abstract quantitative relationship| into a spatial structure| It is about the spatial structure| Even if the Arabic numerals 123456789| You see I just came out in order | Actually in your brain Arrangement | is a spatial structure | What does it mean? It is one, two and three in Arabic numerals | This kind of small number | For Chinese people | He is on the left | Seven, eight and nine are on the right | Of course you can’t see it now | You can imagine it | .

数学是学不会的 | 你学习数学 | 打个比方 | 你看一个做菜视频 | 上面讲了如何炒宫保鸡丁 | 那么这个时候你看完了以后 | 好像自己已经会炒宫保鸡丁 | 其实未心 | 你得把原材料买回来 | 自己现场再炒一遍 | 然后再尝尝这个味道 | 咸了淡甜了 | 够不够味 | 这样才能知道说 | 自己到底学没学会这道宫保鸡丁 | 然后炒菜的过程当中 | 就是一种做研究的过程。Shùxué shì xué bù huì de | nǐ xuéxí shùxué | dǎ gè bǐfāng | nǐ kàn yīgè zuò cài shìpín | shàngmiàn jiǎng liǎo rúhé chǎo gōng bǎo jī dīng | nàme zhège shíhòu nǐ kàn wánliǎo yǐhòu | hǎoxiàng zìjǐ yǐjīng huì chǎo gōng bǎo jī dīng | qíshí wèi xīn | nǐ dé bǎ yuáncáiliào mǎi huílái | zìjǐ xiànchǎng zài chǎo yībiàn | ránhòu zài cháng cháng zhège wèidào | xiánle dàn tiánle | gòu bùgòu wèi | zhèyàng cáinéng zhīdào shuō | zìjǐ dàodǐ xué méi xuéhuì zhè dào gōng bǎo jī dīng | ránhòu chǎocài de guòchéng dāngzhōng | jiùshì yī zhǒng zuò yánjiū de guòchéng.  – You can’t learn mathematics | You learn mathematics | For example | You watch a cooking video | It talks about how to fry Kung Pao chicken | Actually Weixin | You have to buy the raw materials | Fry it again on the spot | Then taste the taste | It is salty and sweet | Is it tasteful enough | Only then can you tell | | Then the process of cooking | is a kind of research process.

另外,我们还需要一位好老师的引导。Lìngwài, wǒmen hái xūyào yī wèi hǎo lǎoshī de yǐndǎo. – In addition, we also need the guidance of a good teacher.

数学是一个非常美好的一个东西 | 非常漂亮的东西 | 为什么我们那么多的同志 | 回忆起自己的中学 | 觉得好像是在受折磨难 | 不怪你们 | 我只能很遗憾地告诉你们 | 你们没碰好老师 | 如果碰到好老师 | 你学数学绝对不亚于你看 《红楼梦》| 更有意思。Shùxué shì yīgè fēicháng měihǎo de yīgè dōngxī | fēicháng piàoliang de dōngxī | wèishéme wǒmen nàme duō de tóngzhì | huíyì qǐ zìjǐ de zhōngxué | juédé hǎoxiàng shì zài shòu zhémó nàn | bù guài nǐmen | wǒ zhǐ néng hěn yíhàn de gàosù nǐmen | nǐmen méi pèng hǎo lǎoshī | rúguǒ pèng dào hǎo lǎoshī | nǐ xué shùxué juéduì bù yǎ yú nǐ kàn hónglóumèng| gèng yǒuyìsi. – Mathematics is a very beautiful thing| A very beautiful thing| Why are there so many of us comrades| Recalling their high school| Feeling like they are being tortured| Don’t blame you| I can only tell you regretfully| Meet a good teacher | If you meet a good teacher | You are definitely as good as watching „A Dream of Red Mansions” | More interesting.

所以增养学生研究能力 | 其实就是要引导他独立思考 | 独立解决问题的能力 | 作为老师 | 不要急于给学生 | 提炼所谓的套路 | 所谓的方法 | 然后就训练学生熟练应用 | 而更应该舍得用足够的时间 | 让学生去自己去思考问题。Suǒyǐ zēng yǎng xuéshēng yánjiū nénglì | qíshí jiùshì yào yǐndǎo tā dúlì sīkǎo | dúlì jiějué wèntí de nénglì | zuòwéi lǎoshī | bùyào jíyú gěi xuéshēng | tíliàn suǒwèi de tàolù | suǒwèi de fāngfǎ | ránhòu jiù xùnliàn xuéshēng shúliàn yìngyòng | ér gèng yīnggāi shědé yòng zúgòu de shíjiān | ràng xuéshēng qù zìjǐ qù sīkǎo wèntí. – Therefore, to enhance students’ research ability| In fact, it is to guide him to think independently| Independent problem-solving ability| As a teacher| Don’t rush to give students | Refine so-called routines| So-called methods| Enough time | Allow students to think for themselves.

允许学生犯错误 | 因为数学的发展本身 | 就是在不断地纠正错误的 | 这样的一个情况下发展起来 | 我们引导学生学习数学 | 实际上是建立他的那种思维的体系 | 这个体系的建立 | 不可能是一帆风顺的。Yǔnxǔ xuéshēng fàn cuòwù | yīn wéi shùxué de fǎ zhǎn běnshēn | jiùshì zài bùduàn dì jiūzhèng cuòwù de | zhèyàng de yīgè qíngkuàng xià fāzhǎn qǐlái | wǒmen yǐndǎo xuéshēng xuéxí shùxué | shíjì shang shì jiànlì tā dì nà zhǒng sīwéi de tǐxì | zhège tǐxì de jiànlì | bù kěnéng shì yīfānfēngshùn de. – Allow students to make mistakes | Because the development of mathematics itself | is constantly correcting mistakes | developed in such a situation | We guide students to learn mathematics | In fact, it is to establish his system of thinking | It can’t be smooth sailing.

老师在教小学的时候 | 往往举的例子 | 都是生活中的一些例子 | 讲的都是他们身边的一些事 | 所以学生兴趣很浓 | 但是到了初中 | 到了高中以后 | 由于升学上面的压力 | 于是他们就逐渐逐渐 | 变得只会解题了 | 时间一长 | 他们就觉得数学比较枯燥 | 纯粹的符号推理论证 | 我个人认为在教学过程中 | 你不把数学背后的 | 历史文化讲给学生听 | 学生怎么能对教学感兴趣呢?Lǎoshī zài jiào xiǎoxué de shíhòu | wǎngwǎng jǔ de lìzi | dōu shì shēnghuó zhōng de yīxiē lìzi | jiǎng de dōu shì tāmen shēnbiān de yīxiē shì | suǒyǐ xuéshēng xìngqù hěn nóng | dànshì dàole chūzhōng | dàole gāozhōng yǐhòu | yóuyú shēngxué shàngmiàn de yālì | yúshì tāmen jiù zhújiàn zhújiàn | biàn dé zhǐ huì jiě tíle | shíjiān yī cháng | tāmen jiù juédé shùxué bǐjiào kūzào | chúncuì de fúhào tuīlǐ lùnzhèng | wǒ gèrén rènwéi zài jiàoxué guòchéng zhōng | nǐ bù bǎ shùxué bèihòu de | lìshǐ wénhuà jiǎng gěi xuéshēng tīng | xuéshēng zěnme néng duì jiàoxué gǎn xìngqù ne? – When teachers teach elementary school | the examples they often give | are examples from life | they talk about things around them | so students are very interested | but when they reach junior high school | after high school | So they gradually | become only able to solve problems | as time goes by | they feel that mathematics is boring | pure symbolic reasoning and argument | I personally think that in the teaching process | you do not tell the history and culture behind mathematics Students Listen | How can students be interested in teaching?

我在教学过程中 | 由于要析书 | 如果随手就画一个平面 | 画一个力的分析中的 | 小车小人这也可以 | 可是尽量能不能 | 把它这个图形画得生动一些 | 画得优美一些 | 画得让学生感兴趣一些 | 让学生的眼亮起来。Wǒ zài jiàoxué guòchéng zhōng | yóuyú yào xī shū | rúguǒ suíshǒu jiù huà yīgè píngmiàn | huà yīgè lì de fēnxī zhōng de | xiǎochē xiǎo rén zhè yě kěyǐ | kěshì jǐnliàng néng bùnéng | bǎ tā zhège túxíng huà dé shēngdòng yīxiē | huà dé yōuměi yì xiē | huà dé ràng xuéshēng gǎn xìngqù yīxiē | ràng xuéshēng de yǎn liàng qǐlái. – In the process of teaching | Because I need to analyze the book | If I draw a plane at random | I draw a little car under the analysis of force | This is also possible | But try my best to | Draw this figure more vividly | Some | Draw to interest students some | To brighten students’ eyes.

函数的曲线是那么样的丰富 | 我就创作了一系列的线条画 | 有的是课堂上面画 | 有的是课前画 | 让学生从人物的线条画中 | 发现曲线 | 我不是专业画画的 | 我可以把这个画定位成数学插图 | 正是因为这样 | 我所追求的就是 | 这幅画中的物的线条感 | 结构感 | 和对数学教学的辅助感。Hán shǔ de qūxiàn shì nàme yàng de fēngfù | wǒ jiù chuàngzuòle yī xìliè de xiàntiáo huà | yǒudeshì kètáng shàngmiàn huà | yǒudeshì kè qián huà | ràng xuéshēng cóng rénwù de xiàntiáo huà zhōng | fāxiàn qūxiàn | wǒ bùshì zhuānyè huà huà de | wǒ kěyǐ bǎ zhège huà dìngwèi chéng shùxué chātú | zhèng shì yīnwèi zhèyàng | wǒ suǒ zhuīqiú de jiùshì | zhè fú huà zhōng de wù de xiàntiáo gǎn | jiégòu gǎn | hé duì shùxué jiàoxué de fǔzhù gǎn. – The curve of the function is so rich | I created a series of line drawings | Some are drawn in class | Some are drawn before class | Positioning this painting as a mathematical illustration| It is because of this| what I am looking for is | the sense of line|line of the objects in this painting|structure| and a sense of assistance to mathematics teaching.

数学中的真善美 | 我们怎么样在课堂教学过程中 | 结合我们的知识点融合进去 | 这就是我们数学教学工作者 | 应当思考的问题。Shùxué zhōng de zhēnshànměi | wǒmen zěnme yàng zài kètáng jiàoxué guòchéng zhōng | jiéhé wǒmen de zhīshì diǎn rónghé jìnqù | zhè jiùshì wǒmen shùxué jiàoxué gōngzuò zhě | yīngdāng sīkǎo de wèntí. – The truth, goodness and beauty in mathematics | How do we integrate our knowledge points in the classroom teaching process | This is the question that we mathematics teaching workers | should think about.

我们可能有一万种 | 学不好数学的理由 | 但没有一个理由 | 可以让我们对数学失去尊重和了解。Wǒmen kěnéng yǒu yī wàn zhǒng | xué bù hǎo shùxué de lǐyóu | dàn méiyǒu yīgè lǐyóu | kěyǐ ràng wǒmen duì shùxué shīqù zūnzhòng hé liǎojiě. – We may have 10,000 | reasons for not learning mathematics | but there is no reason | that can make us lose respect and understanding of mathematics.

从某种意义上讲,数学构筑了我们今天的世界。Cóng mǒu zhǒng yìyì shàng jiǎng, shùxué gòuzhùle wǒmen jīntiān de shìjiè. – In a sense, mathematics makes up our world today.

两千四百年前的伯罗奔尼撒战争中 | 斯巴达士兵捉到了一个波斯探子 | 他身无异物 | 但身上的腰带 | 引起来斯巴达统帅莱桑德的注意 | 莱桑德把腰带缠到他的剑鞘上 | 腰带上的字母 | 便组成了一段完整的文字 | 这就是早期的密码。Liǎng qiān sìbǎi nián qián de bó luó bēn ní sā zhànzhēng zhōng | sī bā dá shìbīng zhuō dàole yīgè bōsī tànzi | tā shēn wú yìwù | dàn shēnshang de yāodài | yǐnqǐ lái sī bā dá tǒngshuài lái sāng dé de zhùyì | lái sāng dé bǎ yāodài chán dào tā de jiàn qiào shàng | yāodài shàng de zìmǔ | biàn zǔchéngle yīduàn wánzhěng de wénzì | zhè jiùshì zǎoqí de mìmǎ. – In the Peloponnesian War 2,400 years ago | Spartan soldiers caught a Persian spy | He had no foreign objects | Wrap the belt around his scabbard | the letters on the belt | form a complete text | this is the early cipher.

 

 

https://www.youtube.com/embed/mmwYi_O4Wvg?start=1189

 

 

 

《被数学选中的人》第3集 Chosen By Mathematics EP3《蒙娜丽莎的微笑》为什么这么美?其实这正和数学的黄金分割有关【CCTV纪录】Bèi shùxué xuǎnzhōng de rén dì 3 jí Chosen By Mathematics EP3méng nà lì shā de wéixiào wèishéme zhème měi? Qíshí zhè zhènghé shùxué de huángjīn fēngē yǒuguān [CCTV jìlù]„The One Chosen by Mathematics” Episode 3 Chosen By Mathematics EP3 „Mona Lisa’s Smile” Why is it so beautiful? In fact, this is related to the golden section of mathematics [CCTV Record]

 

第三集

数学教会了我们什么

Dì sān jí shùxué jiàohuìle wǒmen shénme

– Episode 3

what math has taught us

 

。。。但是大部分人 | 在离开系统的数学教育后 | 能保留的数学知识只乘下四则运算。

… Dànshì dà bùfèn rén | zài líkāi xìtǒng de shùxué jiàoyù hòu | néng bǎoliú de shùxué zhīshì zhǐ chéng xià sìzé yùnsuàn.

– . . . But most people | after leaving a systematic math education | retain only the math knowledge of the next four operations.

我们做的数学题上的数学课到底有什么用?从漫长的数学教育中我们到底学到了什么呢?Wǒmen zuò de shùxué tí shàng de shùxué kè dàodǐ yǒu shé me yòng? Cóng màncháng de shùxué jiàoyù zhōng wǒmen dàodǐ xué dàole shénme ne? – What’s the use of the math class on the math problems we do? What have we learned from a long mathematics education?

 我觉得我喜欢上数学是大概小学的时候。但是那时候对数学理解基本上就是解决一些难题。Wǒ juédé wǒ xǐhuān shàng shùxué shì dàgài xiǎoxué de shíhòu. Dànshì nà shíhòu duì shùxué lǐjiě jīběn shàng jiùshì jiějué yīxiē nántí. – I think I liked math when I was in elementary school. But at that time understanding mathematics was basically solving some difficult problems.

从来没为学数学而痛苦过,不过我其实考最想学的是物理。Cónglái méi wéi xué shùxué ér tòngkǔguò, bùguò wǒ qíshí kǎo zuì xiǎng xué de shì wùlǐ. – I have never suffered from mathematics, but I actually want to study physics the most.

高考的时候数学考了一百四十八 (分)还挺好。Gāokǎo de shíhòu shùxué kǎole yībǎi sìshíbā (fēn) hái tǐng hǎo. – In the college entrance examination, I scored 148 (points) in mathematics, which was pretty good.

特别有成就感 | 然后每次数学考试成绩就很高 | 然后老师就很喜欢你 | 然后就对数学特别特别感兴趣。Tèbié yǒu chéngjiù gǎn | ránhòu měi cì shùxué kǎoshì chéngjī jiù hěn gāo | ránhòu lǎoshī jiù hěn xǐhuān nǐ | ránhòu jiù duì shùxué tèbié tèbié gǎn xìngqù. – There is a special sense of achievement | Then every time you get high marks in the math test | Then the teacher likes you very much | Then you are very interested in mathematics.

小时候记忆很少 | 但是这个记忆我很深刻 | 我会自己在家那种 | 自行车上面铃铛嘛 | 我会按着数到了。Xiǎoshíhòu jìyì hěn shǎo | dànshì zhège jìyì wǒ hěn shēnkè | wǒ huì zìjǐ zàijiā nà zhǒng | zìxíngchē shàngmiàn língdāng ma | wǒ huì àn zhāo shù dàole. – I have very few memories when I was a child | But this memory is very deep for me | I will be at home by myself | The bell on the bicycle | I will count it.

似乎每个人身边 | 都有这样神一般的存在 | 他们生活在大部分人 | 无法受用的数学世界里 | 享受着数学带来的快感 | 大家从同一个起点出发 | 并在启蒙阶段着相同的知识 | 但最终只能相互眺望。Sìhū měi gèrén shēnbiān | dōu yǒu zhèyàng shén yībān de cúnzài | tāmen shēnghuó zài dà bùfèn rén | wúfǎ shòuyong de shùxué shìjiè lǐ | xiǎng shòu zhāo shùxué dài lái de kuàigǎn | dàjiā cóng tóng yīgè qǐdiǎn chūfā | bìng zài qǐméng jiēduànzhe xiāngtóng de zhīshì | dàn zuìzhōng zhǐ néng xiānghù tiàowàng. – It seems that everyone around | has such a god-like existence | they live in a world of mathematics that most people cannot use | enjoy the pleasure of mathematics | everyone starts from the same starting point | and have the same knowledge in the enlightenment stage | But in the end they can only look at each other.

历史上很多伟对数学异常敏感 | 并在青年时代 | 就创造了无比辉煌的成就 | 他们似乎才是真正 | 被数学选中的那些人。Lìshǐ shàng hěnduō wěi duì shùxué yìcháng mǐngǎn | bìng zài qīngnián shídài | jiù chuàng zào liǎo wúbǐ huīhuáng de chéngjiù | tāmen sìhū cái shì zhēnzhèng | bèi shùxué xuǎnzhōng dì nàxiē rén. – Many Wei in history are very sensitive to mathematics | and have created incomparably brilliant achievements in their youth | they seem to be the real | those who were chosen by mathematics.

 十八世纪的欧拉 | 十三岁便入读巴塞尔大学 | 十六岁获得硕士学位 | 他平均每年写出八百多页的论文 | 是第二多产的数学家。Shíbā shìjì de ōu lā | shísān suì biàn rù dú bāsè ěr dàxué | shíliù suì huòdé shuòshì xuéwèi | tā píngjūn měinián xiě chū bābǎi duō yè dì lùnwén | shì dì èr duō chǎn de shùxué jiā. – Euler in the 18th century | Enrolled at the University of Basel at the age of thirteen | Obtained a master’s degree at the age of sixteen | He writes an average of more than 800 pages of theses per year | The second most prolific mathematician.

二十八岁时他的右眼因病近乎失明 | 但这并不影响欧拉在数学上 | 取得了全面而又富有开创性的成就。Èrshíbā suì shí tā de yòu yǎn yīn bìng jìnhū shīmíng | dàn zhè bìng bù yǐngxiǎng ōu lā zài shùxué shàng | qǔdéle quánmiàn ér yòu fùyǒu kāichuàng xìng de chéngjiù. – At the age of twenty-eight he was nearly blind in his right eye | but this did not affect Euler’s comprehensive and groundbreaking achievements in mathematics.

欧拉用几个数学中最基本的常数 | 圆周率 π 和自然数的底 e | 虚数单位 i 也就是负一的开方 | 创造了一个公式 | e 的 i 乘 π 次方等于负一。Ōu lā yòng jǐ gè shùxué zhōng zuì jīběn de chángshù | yuánzhōulǜ p hé zì rán shǔ de dǐ e | xūshù dānwèi i yě jiùshì fù yī de kāi fāng | chuàngzàole yīgè gōngshì | e de i chéng p cì fāng děngyú fù yī. – Euler used several of the most fundamental constants in mathematics | pi and the base e of natural numbers | imaginary unit i, which is the root of negative one | to create a formula | e raised to the power of i times pi equals negative one.

这个简洁而又似乎洞察到 | 宇宙规律的公式 | 深远影响了数学和物理学的发展 | 被后人称为 宇宙最美公式Zhège jiǎnjié ér yòu sìhū dòngchá dào | yǔzhòu guīlǜ de gōngshì | shēnyuǎn yǐngxiǎngle shùxué hé wùlǐ xué de fǎ zhǎn | bèi hòu rén chēng wèi yǔzhòu zuìměi gōngshì”. – This simple and seemingly insightful formula | the laws of the universe | has a profound impact on the development of mathematics and physics | is called „the most beautiful formula of the universe” by later generations.

年轻的法国数学家伽罗瓦 | 十六岁开始研读数学 | 五年后已然获得了非凡的成就 | 他的研究成果被认为是 | 现代群论的开创之作 | 但可惜的是 | 因为爱情他被卷入了一场决斗 | 对方则是法国著名的枪手 | 据说自知必死无疑的伽罗瓦 | 在决斗前一天晚上疯狂写作 |  把自己全部的数学成果记录下来 | 并不时在页边写下 | 我没有时间了 | 第二天 | 伽罗瓦在决斗中中枪身亡 | 年仅二十一岁 | 一八八七年 | 印度的天才数学家拉马努金出生了 | 他家境极为贫穷 | 从没接受过正规的高等数学教育 | 但他却有着超人的直觉洞察力 | 可以找到大量数学关系背后的定律。

Niánqīng de fàguó shùxué jiā jiā luō wǎ | shíliù suì kāishǐ yándú shùxué | wǔ nián hòu yǐrán huòdéle fēifán de chéngjiù | tā de yánjiū chéngguǒ bèi rènwéi shì | xiàndài qún lùn de kāichuàng zhī zuò | dàn kěxí de shì | yīnwèi àiqíng tā bèi juàn rùle yī chǎng juédòu | duìfāng zé shì fàguó zhùmíng de qiāngshǒu | jùshuō zì zhī bìsǐ wúyí de jiā luō wǎ | zài juédòu qián yītiān wǎnshàng fēngkuáng xiězuò | bǎ zìjǐ quánbù de shùxué chéngguǒ jìlù xiàlái | bìng bùshí zài yè biān xiě xià | wǒ méiyǒu shíjiānle | dì èr tiān | jiā luō wǎ zài juédòu zhōng zhōng qiāng shēnwáng | nián jǐn èrshíyī suì | yībābāqī nián | yìndù de tiāncái shùxué jiā lā mǎ nǔ jīn chūshēngle | tā jiājìng jíwéi pínqióng | cóng méi jiēshòuguò zhèngguī de gāoděng shùxué jiàoyù | dàn tā què yǒuzhe chāorén de zhíjué dòngchá lì | kěyǐ zhǎodào dàliàng shùxué guānxì bèihòu de dìnglǜ.

– Galois, a young French mathematician | Started studying mathematics at the age of sixteen | After five years, he has achieved extraordinary achievements | His research results are considered | The pioneering work of modern group theory | But unfortunately | Was involved in a duel | The opponent was a famous French gunman | Galois, who was said to know he was going to die | wrote frantically the night before the duel | recorded all his mathematical results | | „I don’t have time” | The next day | Galois was shot in a duel | Aged only 21 | 1887 | Ramanujan, a genius mathematician in India, was born | Poverty | Never had a formal higher education in mathematics | But he had a superhuman intuitive insight | to find the laws behind a large number of mathematical relationships.

拉马努金独立发现了 | 近三千九百个千奇百怪的数学公式 | 这当中很多都没有留下证明过程 | 以至于后来的数学家们往往会用 | 人生中最宝贵多产的几年时间 | 来验证它们。Lā mǎ nǔ jīn dúlì fāxiànle | jìn sānqiān jiǔbǎi gè qiānqíbǎiguài de shùxué gōngshì | zhè dāngzhōng hěnduō dōu méiyǒu liú xià zhèngmíng guòchéng | yǐ zhìyú hòulái de shùxué jiāmen wǎngwǎng huì yòng | rénshēng zhōng zuì bǎoguì duō chǎn de jǐ nián shíjiān | lái yànzhèng tāmen. – Ramanujan independently discovered | nearly 3,900 strange mathematical formulas | many of which have no proof process | so that later mathematicians often use | the most precious and productive years of life | to verify them.

拉马努金像是一位未来的穿越者。他的数学记事本 | 成为了直到今天 | 科学家们开创分支学科 | 探寻数学规律的宝库。Lā mǎ nǔ jīn xiàng shì yī wèi wèilái de chuānyuè zhě. Tā de shùxué jìshì běn | chéngwéile zhídào jīntiān | kēxuéjiāmen kāichuàng fēnzhī xuékē | tànxún shùxué guīlǜ de bǎokù. – Ramanujan looks like a future traveler. His math notebook | has become to this day | scientists create a branch of disciplines | explore the treasure house of mathematical laws.

 赞颂伟大总是令人心潮澎湃 | 但让我们回到现实 | 忘却这些真正被数学选中的人 | 绝大多数不得不与 | 数学见面的普通人 | 又从数学中学到了什么呢?Zànsòng wěidà zǒng shì lìng rén xīncháo péngpài | dàn ràng wǒmen huí dào xiànshí | wàngquè zhèxiē zhēnzhèng bèi shùxué xuǎnzhōng de rén | jué dà duō shǔ bùdé bù yǔ | shùxué jiànmiàn de pǔtōng rén | yòu cóng shùxué zhōngxué dàole shénme ne? – Celebrating greatness is always heart-warming | But let’s get back to reality | Forget about those who are really chosen by mathematics | The vast majority of ordinary people who have to meet | Mathematics | What have you learned from mathematics?

中国古代有一本非常有名的书 | 叫做 《九章筭术》| 因为它是距今超过二千年了 | 它其实就是今天的小学数学的 | 大部分的内容。Zhōngguó gǔdài yǒuyī běn fēicháng yǒumíng de shū | jiàozuò jiǔ zhāng suàn shù”| yīnwèi tā shì jù jīn chāoguò èrqiān niánle | tā qíshí jiùshì jīntiān de xiǎoxué shùxué de | dà bùfèn de nèiróng. – There was a very famous book in ancient China | It is called „Nine Chapters of Shaping” | because it is more than 2,000 years old | it is actually the content of today’s primary school mathematics | most of the content.

 《九章筭术》是中国古代数学的代表作之一 | 成书于东汉它和比它更古老的 《周髀算经》一样 | 最早的成书时间和作者 | 都无从可考。Jiǔ zhāng suàn shù” shì zhōngguó gǔdài shùxué de dàibiǎozuò zhī yī | chéngshū yú dōnghàn tā hé bǐ tā gèng gǔlǎo de zhōu bì suàn jīng yīyàng | zuìzǎo de chéngshū shíjiān hé zuòzhě | dōu wúcóng kě kǎo. – „Jiuzhang Zhushu” is one of the representative works of ancient Chinese mathematics | It was written in the Eastern Han Dynasty and it is the same as „Zhou Bi Suanjing”, which is older than it. The earliest time and author of the book are unknown.

一般认为它是从先秦到西汉中叶 | 经过众多学者 | 编纂修改而成的一部数学著作。Yībān rènwéi tā shì cóng xiānqín dào xīhàn zhōngyè | jīngguò zhòngduō xuézhě | biānzuǎn xiūgǎi ér chéng de yī bù shùxué zhùzuò. – It is generally believed that it is a mathematical work edited and revised by many scholars from the pre-Qin period to the middle of the Western Han Dynasty.

《九章算术》提出了依次是方田粟米衰分小广 | 商功均输盈不足方程勾股 | 前几章主要是生产生活的实际应用 | 后面的盈不足 成程 和 勾股 | 则涉及了方程方程组 | 以及几何问题 | 比如盈不足第一题 | 今有共买物 | 人出八盈三 | 人出七不足四 | 问人数物价各几何 | 答日 | 七人物价五十三 | 解答这种方程的方法 | 被称为 盈不足术 是现代 线性插值法 的鼻祖。

Jiǔ zhāng suànshù” tíchūle yīcì shì fāng tián sùmǐ shuāi fēn xiǎo guǎng | shāng gōng jūn shū yíng bùzú fāngchéng gōu gǔ | qián jǐ zhāng zhǔyào shi shēngchǎn shēnghuó de shíjì yìngyòng | hòumiàn de yíng bùzú chéng chéng hé gōu gǔ | zé shèjíle fāngchéng fāngchéng zǔ | yǐjí jǐhé wèntí | bǐrú yíng bùzú dì yī tí | jīn yǒu gòng mǎi wù | rén chū bā yíng sān | rén chū qī bùzú sì | wèn rénshù wùjià gè jǐhé | dá rì | qī rénwù jià wǔshísān | jiědá zhè zhǒng fāngchéng de fāngfǎ | bèi chēng wèi yíng bùzú shù” shì xiàndài xiànxìng chāzhí de bízǔ.

„Nine Chapters of Arithmetic” proposes the following in order: Fangtian corn decline and small wide | business success, loss, profit and deficiency equation Pythagorean | The first few chapters are mainly about the practical application of production and life | solve the equation system | and geometric problems | such as the first question of insufficient surplus | „there are a total of things to buy | ” | The method of solving this equation | is called the „underfill technique” and is the originator of the modern „linear interpolation method”.

《九章筭术》中的 正负术 | 也就是正负数的加减运算法则 | 表明中国人很早就开始使用负数 | 而印度则在七世纪才开始使用 | 西方就更晚了 | 另外一种 开方术 | 也就是现代意义上的开方 | 这说明我们的祖先 | 已经触碰到了无理数的边缘 | 这与杀腊文明着相似的认知。Jiǔ zhāng suàn shù” zhōng de zhèng fùshù” | yě jiùshì zhèng fù shǔ de jiā jiǎn yùnsuàn fǎzé | biǎomíng zhōngguó rén hěn zǎo jiù kāishǐ shǐyòng fù shù | ér yìndù zé zài qī shìjì cái kāishǐ shǐyòng | xīfāng jiù gèng wǎnle | lìngwài yī zhǒng kāi fāngshù” | yě jiùshì xiàndài yìyì shàng de kāi fāng | zhè shuōmíng wǒmen de zǔxiān | yǐjīng chù pèng dào liǎo wú lǐ shǔ de biānyuán | zhè yǔ shā là wénmíngzhe xiāngsì de rèn zhī. – The „Positive and Negative Technique” in „Nine Chapters of Reincarnation” | that is, the addition and subtraction of positive and negative numbers | shows that the Chinese began to use negative numbers very early | while India began to use them in the seventh century | the West was even later | Another kind of „square prescription” | that is, the prescription in the modern sense | This shows that our ancestors | have touched the edge of irrational numbers | This is similar to the cognition of killing La civilization.

我们另外也知道 | 在两千多年前 | 有一本流传至今的 | 古希腊的数学名著 | 就是欧几里得的《原本》| 主要内容就是我们今天所说的 | 平面几何与立体几何 | 这个基本上就是 | 我们上了初中以后学习的 | 就是几何学 | 可以这样来进 | 从小学开始直到初中的 | 绝大多数内容 | 基本上对应在数学发展过程当中 | 就是对应十六世纪以前的数学 | 然后进入十七世纪 | 因为数学有几个重要的创造 | 特别突出的就是解析几何 | 微积分概率论这样的几个领域 | 另外数论也得到了比较大的发展 | 我们说解析几何 | 现在差不多是到了高中学习的内容 | 而微积分现在中学里面学一点点 | 更主要的内容 | 就要等到读大学本科的时候 | 才会去学习了。

Wǒmen lìngwài yě zhīdào | zài liǎng qiān duō nián qián | yǒuyī běn liúchuán zhìjīn de | gǔ xīlà de shùxué míngzhù | jiùshì ōu jǐ lǐ dé de yuánběn| zhǔyào nèiróng jiùshì wǒmen jīntiān suǒ shuō de | píngmiàn jǐhé yǔ lìtǐ jǐhé | zhège jīběn shàng jiùshì | wǒmen shàngle chūzhōng yǐhòu xuéxí de | jiùshì jǐhé xué | kěyǐ zhèyàng lái jìn | cóng xiǎoxué kāishǐ zhídào chūzhōng de | jué dà duōshù nèiróng | jīběn shàng duìyìng zài shùxué fāzhǎn guòchéng dāngzhōng | jiùshì duìyìng shíliù shìjì yǐqián de shùxué | ránhòu jìnrù shíqī shìjì | yīn wéi shùxué yǒu jǐ gè zhòngyào de chuàngzào | tèbié túchū de jiùshì jiěxī jǐhé | wéi jīfēn gàilǜ lùn zhèyàng de jǐ gè lǐngyù | lìngwài shùlùn yě dédàole bǐjiào dà de fǎ zhǎn | wǒmen shuō jiěxī jǐhé | xiànzài chàbùduō shì dàole gāozhōngxuéxí de nèiróng | ér wéi jīfēn xiànzài zhōng xué lǐmiàn xué yī diǎndiǎn | gèng zhǔyào de nèiróng | jiù yào děngdào dú dàxué běnkē de shíhòu | cái huì qù xuéxíle.

– We also know that | more than 2,000 years ago | there is an ancient Greek mathematical masterpiece | that is Euclid’s „Original” | the main content is what we call today | plane geometry and solid geometry | this Basically | what we learned after entering junior high school | is geometry | can be entered like this | from elementary school to junior high school | most of the content | basically corresponds to the process of mathematics development | | Then entered the seventeenth century | Because mathematics has several important creations | The most prominent is analytic geometry | Several fields such as calculus and probability theory | In addition, number theory has also been relatively developed | We say analytic geometry | It is almost the same now It is the content of learning in high school| and calculus is now learned a little in middle school| The more main content| will have to wait until the time of undergraduate study| to learn.

绝对值

初中数学

正负数

Juéduì zhí chūzhōng shùxué zhèng fù shù

– absolute value

Junior high school mathematics

positive and negative numbers

还记得这些数学公式和定理吗?Hái jìdé zhèxiē shùxué gōngshì hé dìnglǐ ma? – Remember these mathematical formulas and theorems?

幂,立方根,数列,有理数,平方根,因式分解,实数,一次函数,一元二次方程求根公式,指数函数,正弦定理,余弦定理, 对数函数, 复数, 等比数列, 等差数列 Mì, lìfānggēn, shùliè, yǒulǐshù, píngfānggēn, yīn shì fēnjiě, shíshù, yīcì hánshù, yīyuán èr cì fāngchéng qiú gēn gōngshì, zhǐshù hánshù, zhèngxián dìnglǐ, yúxián dìnglǐ, duì shù hánshù, fùshù, děng bǐ shùliè, děng chā shùliè  – Power, cube root, sequence of numbers, rational numbers, square root, factorization, real numbers, linear function, quadratic equation in one variable, exponential function, sine law, cosine law, logarithmic function, complex number, proportional sequence, arithmetic sequence

这只是我们学过的 | 众多数学知识中很小的一部分 | 如果觉得既熟悉又陌生 | 这种感觉是对的 | 因为在日常生活中 | 很多知识从来都没有被用到过 | 四则运算几乎就解决了所有问题 | 可能很多人都有过这样的疑问 | 既然根本用不上 | 何必要学那么多呢? | 学的时间是不是也大长了些呢?Zhè zhǐshì wǒmen xuéguò de | zhòngduō shùxué zhīshì zhōng hěn xiǎo de yībùfèn | rúguǒ juédé jì shúxī yòu mòshēng | zhè zhǒng gǎnjué shì duì de | yīnwèi zài rìcháng shēnghuó zhōng | hěnduō zhīshì cónglái dōu méiyǒu bèi yòng dàoguò | sìzé yùnsuàn jīhū jiù jiějuéle suǒyǒu wèntí | kěnéng hěnduō rén dōu yǒuguò zhèyàng de yíwèn | jìrán gēnběn yòng bù shàng | hébì yào xué nàme duō ne? | Xué de shíjiān shì bùshì yě dà zhǎngle xiē ne? – This is only what we have learned | a very small part of the many mathematics knowledge | if it feels both familiar and unfamiliar | this feeling is right | because in daily life | a lot of knowledge has never been used | four arithmetic operations are almost Solved all problems | Many people may have had such questions | Since it is not used at all | Why do you need to learn so much? | Has the study time been longer?

 我觉得总体而言并不能说很长 | 如果非要说的话 | 甚至我觉得有一些短 | 我们学了九年甚至十二年的数学 | 也仅仅学到了微积分之前 | 这也只是十六世纪的数学 | 那么当代社会 | 我们要求一个当代的现代人 | 要以人人掌握微积分 | 为标准的话 | 那么我们受到的训练可能还不够。Wǒ juédé zǒngtǐ ér yán bìng bùnéng shuō hěn zhǎng | rúguǒ fēi yào shuō dehuà | shènzhì wǒ juédé yǒu yīxiē duǎn | wǒmen xuéle jiǔ nián shènzhì shíèr nián de shùxué | yě jǐnjǐn xué dàole wéi jīfēn zhīqián | zhè yě zhǐshì shíliù shìjì de shùxué | nàme dāngdài shèhuì | wǒmen yāoqiú yīgè dāngdài de xiàndài rén | yào yǐ rén rén zhǎngwò wéi jīfēn | wèi biāozhǔn dì huà | nàme wǒmen shòudào de xùnliàn kěnéng hái bùgòu. – I don’t think it’s very long in general| If you have to say it| I even think it’s a little short| We studied mathematics for nine or even twelve years| And only before calculus| It was only the sixteenth century the mathematics of | then contemporary society | we require a contemporary modern | if everyone masters calculus | as a standard | then we may not be trained enough.

英国成年人因为计算能力 | 算术能力的问题 | 导致每年损失二十四亿英镑 | 占到 GDP 的百分之零点一七 | 这个数字我可记得非常地清楚 | 破坏作用是非常大 | 所以说中国的 | 计算基础知识的教学很扎实 | 我觉得很好 | 但是这种扎实的教学来源 | 不能靠学生去做难题 | 做非常复杂的题日 | 做偏题怪题 | 而应该是建立在 | 对数学概念的理解之上。Yīngguó chéngnián rén yīnwèi jìsuàn nénglì | suànshù nénglì de wèntí | dǎozhì měinián sǔnshī èrshísì yì yīngbàng | zhàn dào GDP de bǎi fēn zhī líng diǎn yīqī | zhège shùzì wǒ kě jìdé fēicháng de qīngchǔ | pòhuài zuòyòng shì fēicháng dà | suǒyǐ shuō zhōngguó de | jìsuàn jīchǔ zhīshì de jiàoxué hěn zhāshi | wǒ juédé hěn hǎo | dànshì zhè zhǒng zhāshi de jiàoxué láiyuán | bùnéng kào xuéshēng qù zuò nántí | zuò fēicháng fùzá de tí rì | zuò piāntí guài tí | ér yīnggāi shì jiànlì zài | duì shùxué gàiniàn de lǐjiě zhī shàng. – Adults in the UK lose £2.4 billion a year because of their numeracy | problems with arithmetic skills | 0.17% of GDP | I remember this number very clearly | Chinese | The teaching of basic computing knowledge is very solid | I think it is very good | But this kind of solid teaching source | Can’t rely on students to do difficult problems | Do very complicated questions | understanding of mathematical concepts.

应考能力增强 | 各种各样的题型你都接触到了 | 这个数学没多但是你的负担重了 | 对于一个学习者个体来说 | 那肯定负担重了就是多了 | 这个多不是质的多。Yìngkǎo nénglì zēngqiáng | gè zhǒng gè yàng de tí xíng nǐ dōu jiēchù dàole | zhège shùxué méi duō dànshì nǐ de fùdān zhòngle | duìyú yīgè xuéxí zhě gètǐ lái shuō | nà kěndìng fùdān zhòngle jiùshì duōle | zhège duō bùshì zhì de duō. – Enhanced ability to take exams | You have been exposed to all kinds of question types | There is not much mathematics, but your burden is heavy | For an individual learner | .

a 加 b 括号的平方 | 这样的一个完全平方公式 | 有用吗 | 谁有多少人一辈子 | 还会用到这个公式呢 | 这样类似于这样的公式 | 如果没有用 | 我们为什么要学它呢 | 甚至我们还要跟它相关的题日 | 要演练很多很多呢 | 我想这可能都是 | 比较狭隘的一种看法 | 或者比较急功近利 | 因为现在大家都知道了 | 我们知识的学习 | 实际上是要以它作为载体 | 我们要形成我们的学科的素养。

A jiā b guāhào de píngfāng | zhèyàng de yīgè wánquán píngfāng gōngshì | yǒuyòng ma | shéi yǒu duōshǎo rén yībèizi | hái huì yòng dào zhège gōngshì ne | zhèyàng lèisì yú zhèyàng de gōngshì | rúguǒ méiyǒu yòng | wǒmen wèishéme yào xué tā ne | shènzhì wǒmen hái yào gēn tā xiāngguān de tí rì | yào yǎnliàn hěnduō hěnduō ne | wǒ xiǎng zhè kěnéng dōu shì | bǐjiào xiáài de yī zhǒng kànfǎ | huòzhě bǐjiào jígōngjìnlì | yīnwèi xiànzài dàjiā dōu zhīdàole | wǒmen zhīshì de xuéxí | shíjì shang shì yào yǐ tā zuòwéi zàitǐ | wǒmen yào xíngchéng wǒmen de xuékē de sùyǎng.

– a plus b square of parentheses | is such a perfect square formula useful | how many people live | will they use this formula | such a formula like this | if it doesn’t work | why should we learn it | even We also have to do some questions related to it | There are many, many exercises to do | I think this may be | a narrow view | or a quick success | because everyone knows it now | Using it as a carrier | We want to form the literacy of our disciplines.

当你把所有的公式图表 | 把这些所有的知识 | 具体的知识忘掉之后 | 最后你能沉淀下来的东西 | 其实就是数学教育 | 所赋予你的东西。Dāng nǐ bǎ suǒyǒu de gōngshì túbiǎo | bǎ zhèxiē suǒyǒu de zhīshì | jùtǐ de zhīshì wàngdiào zhīhòu | zuìhòu nǐ néng chéndiàn xiàlái de dōngxī | qíshí jiùshì shùxué jiàoyù | suǒ fùyǔ nǐ de dōngxī. – When you forget all the formulas and charts | all the knowledge | specific knowledge | what you can finally settle | is actually what math education | gives you.

数学真的在潜移默化地影响着每个人吗?Shùxué zhēn de zài qiányímòhuà dì yǐngxiǎngzhe měi gèrén ma? – Is mathematics really affecting everyone subtly?

它是否已经渗透到了我们的日常行为和意识之中。Tā shìfǒu yǐjīng shèntòu dàole wǒmen de rìcháng xíngwéi hé yìshí zhī zhōng. – Whether it has penetrated into our daily behavior and consciousness.

或者我们早已习以为常以至于不知不觉。Huòzhě wǒmen zǎoyǐ xíyǐwéicháng yǐ zhìyú bùzhī bù jué. – Or we’ve gotten so used to it that we don’t even realize it.

圆周率很好理解 | 圆周长与直径的比值 | 但它又很神秘 | 似乎暗合着某些宇宙的规律。Yuánzhōulǜ hěn hǎo lǐjiě | yuánzhōu cháng yǔ zhíjìng de bǐzhí | dàn tā yòu hěn shénmì | sìànhézhù mǒu xiē yǔzhòu de guīlǜ. – Pi is well understood | the ratio of the circumference of a circle to its diameter | but it is mysterious | it seems to coincide with some laws of the universe.

它带出了无理数的概念 | 这些概念和规律 | 对一个小学生来说是难以理解的 | 但数学世界就是从这里 | 真正向我们敞开了大门。Tā dài chū liǎo wú lǐ shǔ de gàiniàn | zhèxiē gàiniàn hé guīlǜ | duì yīgè xiǎoxuéshēng lái shuō shì nányǐ lǐjiě de | dàn shùxué shìjiè jiùshì cóng zhèlǐ | zhēnzhèng xiàng wǒmen chǎngkāile dàmén. – It brings out the concept of irrational numbers | these concepts and laws | incomprehensible to a schoolboy | but from here the world of mathematics really opens its doors to us.

黄金分割 | 是人们津津乐道美学问题 | 它的数学原理 | 早在公元前四世纪的古希腊 | 就被发现了 | 如果把一条线段 AB 分割为两部分 | 较长部分与全长的比值 | 和较短部分与较长部分的比值 | 是相等的 | 这个比值约为零点六一八比一 | 如果后过来相比 | 比值则约为一点六一八比一。Huángjīn fēngē | shì rénmen jīnjīn lè dào měixué wèntí | tā de shùxué yuánlǐ | zǎo zài gōngyuán qián sì shìjì de gǔ xīlà | jiù pī fà xiàn le | rúguǒ bǎ yītiáo xiànduàn AB fēngē wèi liǎng bùfèn | jiào zhǎng bùfèn yǔ quán zhǎng de bǐzhí | hé jiào duǎn bùfèn yǔ jiào zhǎng bùfèn de bǐzhí | shì xiāngděng de | zhège bǐzhí yuē wéi líng diǎn liùyībā bǐ yī | rúguǒ hòu guòlái xiāng bǐ | bǐzhí zé yuē wéi yī diǎn liùyībā bǐ yī. – The golden section | is an aesthetic problem that people are talking about | its mathematical principle | as early as the fourth century BC in ancient Greece | was discovered | if a line segment AB is divided into two parts | the ratio of the longer part to the full length | and the ratio of the shorter part to the longer part | is equal | this ratio is about 0.618 to one | if compared later | the ratio is about 1.618 to one.

把黄金分割引申到平面图形上 | 就产生了黄金比例 | 一个长方形长度减去宽度后 | 形成一个新的长方形 | 那么原来长方形长与宽的比例 | 这个比例就是黄金分割的比例 | 一点儿六一八比一 | 这是一个神奇的比例 | 因为符合这一比例的物体 | 会给人天然的美感。Bǎ huángjīn fēngē yǐnshēn dào píngmiàn túxíng shàng | jiù chǎnshēngle huángjīn bǐlì | yīgè chángfāngxíng chángdù jiǎn qù kuāndù hòu | xíngchéng yīgè xīn de chángfāngxíng | nàme yuánlái chángfāngxíng zhǎng yǔ kuān de bǐlì | zhège bǐlì jiùshì huángjīn fēngē de bǐlì | yīdiǎn er liùyībā bǐ yī | zhè shì yīgè shénqí de bǐlì | yīnwèi fúhé zhè yī bǐlì de wùtǐ | huì jǐ rén tiānrán dì měigǎn. – Extending the golden section to a flat graphic | produces the golden ratio | after subtracting the width of a rectangle from the length | forms a new rectangle | then the ratio of the length and width of the original rectangle | this ratio is the golden ratio | Eight to one | This is a magic ratio | because objects that fit this ratio | give people a natural beauty.

这种美感不因人是否 | 了解数学原理而存在 | 比如蒙丽莎脸的宽度与长 | 额头到眼睛 | 以及眼睛到下巴的比 | 都符合黄金比例。Zhè zhǒng měigǎn bù yīn rén shìfǒu | liǎo xiè shùxué yuánlǐ ér cúnzài | bǐrú méng lì shā liǎn de kuāndù yǔ zhǎng | étóu dào yǎnjīng | yǐjí yǎnjīng dào xiàbā de bǐ | dōu fúhé huángjīn bǐlì. – This kind of beauty does not exist because of whether people | understand the principles of mathematics | For example, the width and length of Mon Lisa’s face | forehead to eyes | and the ratio of eyes to chin | all conform to the golden ratio.

十六比九屏幕的电视机 | 比四比三的看得更舒服 | 那是因为更接近黄金比例。Shíliù bǐ jiǔ píngmù de diànshì jī | bǐ sì bǐ sān de kàn dé gèng shūfú | nà shì yīnwèi gèng jiējìn huángjīn bǐlì. – Sixteen to nine screen TVs | More comfortable to watch than four to three | That’s because it’s closer to the golden ratio.

雅典帕特农神庙 | 巴黎圣母院的长宽比 | 小提琴的长宽比 | 五角星中所有线段之间的长度关系 | 都符合黄金分割比 | 具体到女孩穿多高的高跟鞋 | 才能让自己符合黄金比例呢?| 就是让全社会让全身与下半身 | 也就是肚脐到脚底的高度 | 具有一点儿八六一八的比例 | 而雕塑 《断臂的维纳斯》| 正好符合这一些例。Yǎdiǎn pà tè nóng shén miào | bālí shèngmǔ yuàn de cháng kuān bǐ | xiǎotíqín de cháng kuān bǐ | wǔjiǎo xīng zhōng suǒyǒu xiànduàn zhī jiān de chángdù guānxì | dōu fúhé huángjīn fēngē bǐ | jùtǐ dào nǚhái chuān duō gāo de gāogēnxié | cáinéng ràng zìjǐ fúhé huángjīn bǐlì ne?| Jiùshì ràng quán shèhuì ràng quánshēn yǔ xiàbànshēn | yě jiùshì dùqí dào jiǎodǐ de gāodù | jùyǒu yīdiǎn er bāliùyībā de bǐlì | ér diāosù duàn bì de wéi nà| zhènghǎo fúhé zhè yīxiē lì. – The Parthenon in Athens | The aspect ratio of Notre Dame de Paris | The aspect ratio of the violin | The length relationship between all line segments in the five-pointed star | All in line with the golden ratio | What about the golden ratio? | It is to let the whole society let the whole body and the lower body | that is, the height from the navel to the soles of the feet | have a proportion of 18618 | and the sculpture „Venus with Broken Arm” | is exactly in line with these examples.

当我们拍出一张 | 自我感觉良好的照片 | 这种良好的感觉 | 也许正是因为照片的构图 | 符合黄金分割比例 | 这便是数学对人潜移默化的影响。Dāng wǒmen pāi chū yī zhāng | zìwǒ gǎnjué liánghǎo de zhàopiàn | zhè zhǒng liánghǎo de gǎnjué | yěxǔ zhèng shì yīn wéi zhàopiàn de gòutú | fúhé huángjīn fēngē bǐlì | zhè biàn shì shùxué duì rén qiányímòhuà de yǐngxiǎng. – When we take a | feel good photo | this good feeling | maybe it is because of the composition of the photo | in accordance with the golden ratio | this is the subtle influence of mathematics on people.

我觉得数学在国民教育当中 | 一个很重要的角色 | 就在于通过数学的训练 | 可以让一个人的逻辑思维 | 变得比较强 | 然后推理能力变得比较强 | 而很多事情也能够培养一个人 | 所谓在乎根据的这种品质 | 思维品质 | 很多人说这品质重要吗? | 我跟各位报告 | 如果一个人的想法 | 他的做法也的所谓判断 | 是一个没有根据的 | 他很难在这个社会上活得很好。Wǒ juédé shùxué zài guómín jiàoyù dāngzhōng | yīgè hěn zhòngyào de juésè | jiù zàiyú tōngguò shùxué de xùnliàn | kěyǐ ràng yīgè rén de luójí sīwéi | biàn dé bǐjiào qiáng | ránhòu tuīlǐ nénglì biàn dé bǐjiào qiáng | ér hěnduō shìqíng yě nénggòu péiyǎng yīgè rén | suǒwèi zàihū gēnjù de zhè zhǒng pǐnzhí | sīwéi pǐnzhí | hěnduō rén shuō zhè pǐnzhí zhòngyào ma? | Wǒ gēn gèwèi bàogào | rúguǒ yīgè rén de xiǎngfǎ | tā de zuòfǎ yě de suǒwèi pànduàn | shì yīgè méiyǒu gēnjù de | tā hěn nán zài zhège shèhuì shàng huó dé hěn hǎo. – I think mathematics plays a very important role in national education| is that through the training of mathematics| it can make a person’s logical thinking| become stronger| and then the reasoning ability becomes stronger| and many things can also cultivate a person | This quality of the so-called caring about the basis | The quality of thinking | Many people say that this quality is important? | I will report to you | If a person’s thoughts | the so-called judgments of his actions | are unfounded | it is difficult for him to live well in this society.

数学的理性最重要的体现就是用数目字说话。用数目字说话能够言之有据 | 而且步步有据 | 因为用数字做依据 | 一般认为是比较扎实的。Shùxué de lǐxìng zuì zhòngyào de tǐxiàn jiùshì yòng shùmùzì shuōhuà. Yòng shùmùzì shuōhuà nénggòu yán zhī yǒu jù | érqiě bù bù yǒu jù | yīnwèi yòng shùzì zuò yījù | yībān rènwéi shì bǐjiào zhāshi de. – The most important manifestation of mathematical rationality is to speak with numbers. Speaking with numbers can be well-founded | and every step of the way | because using numbers as a basis | is generally considered to be more solid.

那更深一个层次 | 数学有没有有别于其它学科 | 其它学科没有 | 只有数学学科有的 | 如果那个东西能够提炼出来的话 | 它对学生理性思维的养成 | 肯定有数学的作用力。Nà gēngshēn yīgè céngcì | shùxué yǒu méiyǒu yǒu bié yú qítā xuékē | qítā xuékē méiyǒu | zhǐyǒu shùxué xuékē yǒu de | rúguǒ nàgè dōngxī nénggòu tíliàn chūlái dehuà | tā duì xuéshēng lǐxìng sīwéi de yǎng chéng | kěndìng yǒu shùxué de zuòyòng lì. – Then a deeper level | Is mathematics different from other subjects | Other subjects do not | Only mathematics subjects have it | If that thing can be extracted | It can cultivate students’ rational thinking | It must have the effect of mathematics.

数学有其它学科没有 | 唯独数学学科有的 | 两个一个叫抽象 | 一个叫推理。Shùxué yǒu qítā xuékē méiyǒu | wéi dú shùxué xuékē yǒu de | liǎng gè yīgè jiào chōuxiàng | yīgè jiào tuīlǐ. – There are no other subjects in mathematics | only mathematics subjects have | two are called abstraction | one is called reasoning.

理科的其它学科没有研究抽象的 | 物理, 化学是靠实验的 | 生物也是靠实验的看得见算是吧 | 你包括纳米 | 纳米那么微小 | 你得把它拍下来 | 才算你发现了新的纳米成分 | 但是数学不是那样 | 数学一个含有未知量的等式 | 就概括了世间万物 | 所以数学的抽象 | 是其它学科没有的特点。Lǐkē de qítā xuékē méiyǒu yánjiū chōuxiàng de | wùlǐ, huàxué shì kào shíyàn de | shēngwù yěshì kào shíyàn de kàn dé jiàn suànshì ba | nǐ bāokuò nàmǐ | nàmǐ nàme wéixiǎo | nǐ dé bǎ tā pāi xiàlái | cái suàn nǐ fāxiànle xīn de nàmǐ chéngfèn | dànshì shùxué bùshì nàyàng | shùxué yīgè hányǒu wèizhī liàng de děng shì | jiù gàikuòle shìjiān wànwù | suǒyǐ shùxué de chōuxiàng | shì qítā xuékē méiyǒu de tèdiǎn. – Other disciplines of science do not study abstract | physics and chemistry rely on experiments | biology also relies on experiments to see it | you include nanometers | nanometers are so tiny | you have to photograph it | Nanocomponents | But mathematics is not like that | Mathematics contains an equation with unknown quantities | It summarizes everything in the world | So the abstraction of mathematics | is a feature that other disciplines do not have.

反正我们这些人崇拜数学的人 | 就是它是讲道理的一种学科 | 它什么东西 | 它自己又己的一套公理体系 | 你要找到逻辑推理一步一步 | 从 a 可以推到 b | b 可以推到 c | 你要这么做出来的。Fǎnzhèng wǒmen zhèxiē rén chóngbài shùxué de rén | jiùshì tā shì jiǎng dàolǐ de yī zhǒng xuékē | tā shénme dōngxī | tā zìjǐ yòu jǐ de yī tào gōnglǐ tǐxì | nǐ yào zhǎodào luójí tuīlǐ yībù yībù | cóng a kěyǐ tuī dào b | b kěyǐ tuī dào c | nǐ yào zhème zuò chūlái de. – Anyway, those of us who worship mathematics| it is a discipline of reason| what is it| its own set of axioms| you have to find logical reasoning step by step| from a can be pushed to b | b can be Push to c | you’re going to do it out.

数学的逻辑推理思想 | 在两千年前就已确立 | 古希腊数学家欧几里得 | 所著的《几何原本》| 归纳了自公元前七世纪开始 | 几百年间的几何和数论知识 | 在书中 | 欧几里得开创性地 | 使用演绎推理的方式进行数学证明。Shùxué de luójí tuīlǐ sīxiǎng | zài liǎng qiānnián qián jiù yǐ quèlì | gǔ xīlà shùxué jiā ōu jǐ lǐ dé | suǒzhe de jǐhé yuánběn| guīnàle zì gōngyuán qián qī shìjì kāishǐ | jǐ bǎi nián jiān de jǐhé hé shùlùn zhīshì | zài shū zhōng | ōu jǐ lǐ dé kāichuàng xìng dì | shǐyòng yǎnyì tuīlǐ de fāngshì jìnxíng shǔ xué zhèngmíng. – The idea of logical reasoning in mathematics| Established two thousand years ago| Euclid, the ancient Greek mathematician| The Elements of Geometry| Summarizes the knowledge of geometry and number theory over hundreds of years since the seventh century BC| In the book | Euclid pioneered | the use of deductive reasoning for mathematical proofs.

欧几里得首先提出了 | 五个公理五个公设 | 以及二十三条定义 | 他认为这些是无可辩驳的常理 | 比如 彼此能重合的物体是全等的 | 再比如 凡是直角都相等 | 接着他利用这些条件 | 对第一个命题进行证明 | 之后便以第一个命题为条件 | 结合公理公设和定义 | 继续证明第二个 | 最终将全部命题依次证明完毕。Ōu jǐ lǐ dé shǒuxiān tíchūle | wǔ gè gōnglǐ wǔ gè gōngshè | yǐjí èrshísān tiáo dìngyì | tā rènwéi zhèxiē shì wú kě biànbó de chánglǐ | bǐrú “bǐcǐ néng chónghé de wùtǐ shì quán děng de” | zài bǐrú “fánshì zhíjiǎo dōu xiāngděng” | jiēzhe tā lìyòng zhèxiē tiáojiàn | duì dì yī gè mìngtí jìnxíng zhèngmíng | zhīhòu biàn yǐ dì yī gè mìngtí wèi tiáojiàn | jiéhé gōnglǐ gōngshè hé dìngyì | jìxù zhèngmíng dì èr gè | zuìzhōng jiāng quánbù mìngtí yīcì zhèngmíng wánbì. – Euclid first put forward | five axioms and five postulates | and twenty-three definitions | he believed that these were irrefutable common sense | such as „objects that can coincide with each other are congruent” | All are equal” | Then he uses these conditions | to prove the first proposition | and then uses the first proposition as a condition | combines the axioms and definitions | continues to prove the second | and finally proves all the propositions in turn.

欧几里得几何的五个公理

1。过相异两点,能作且只能作一直线。

2。线段 (有限直线)可以任意地延长。

3。 以任一点为圆心,任意长为半径,可作一圆。

4。 凡是直角都相等。

5。 两直线被第三条直线所截, 如果同侧两内角和小于两个直角,则两直线会在该侧相交。

Ōu jǐ lǐ dé jǐhé de wǔ gè gōnglǐ 1.Guò xiāng yì liǎng diǎn, néng zuò qiě zhǐ néng zuò yīzhíxiàn. 2. Xiànduàn (yǒuxiàn zhíxiàn) kěyǐ rènyì dì yáncháng. 3. Yǐ rèn yīdiǎn wéi yuánxīn, rènyì zhǎng wèi bànjìng, kě zuò yī yuán. 4. Fánshì zhíjiǎo dōu xiāngděng. 5. Liǎng zhíxiàn bèi dì sān tiáo zhíxiàn suǒ jié, rúguǒ tóng cè liǎng nèijiǎo hé xiǎoyú liǎng gè zhíjiǎo, zé liǎng zhí xiàn huì zài gāi cè xiàngjiāo.

– Five Axioms of Euclidean Geometry

  1. Passing through two different points, it can make and can only make a straight line.
  2. Line segments (finite straight lines) can be extended arbitrarily.
  3. With any point as the center and any length as the radius, a circle can be made.
  4. All right angles are equal.
  5. Two lines are intercepted by a third line. If the sum of the two interior angles on the same side is less than two right angles, the two lines will meet on that side.

 

今天逻辑推理不仅在悬疑影片中 | 被极度放大 | 对每个人来说 | 当处理一件较为复杂的事情时 | 我们都会自发地 | 调用头脑中的逻辑推理能力 | 以寻求一个最会理的解决办法。Jīntiān luójí tuīlǐ bùjǐn zài xuányí yǐngpiàn zhōng | bèi jídù fàngdà | duì měi gèrén lái shuō | dāng chǔlǐ yī jiàn jiàowéi fùzá de shìqíng shí | wǒmen dūhuì zìfā dì | diàoyòng tóunǎo zhōng de luójí tuīlǐ nénglì | yǐ xúnqiú yīgè zuì huì lǐ de jiějué bànfǎ. – Today’s logical reasoning is not only in suspense films | is extremely magnified | for everyone | when dealing with a more complex matter | we will spontaneously | invoke the logical reasoning ability in our minds | to seek the most reasonable solution Method.

这种能力也许就和你从小受到的数学教育相关。Zhè zhǒng nénglì yěxǔ jiù hé nǐ cóngxiǎo shòudào de shùxué jiàoyù xiāngguān. – This ability may be related to the mathematics education you received from childhood.

华东师范大数学系的师生们正在排练一部新的数学话剧《让我们从 <几何原本> 谈起》。Huádōng shīfàn dà shùxué xì de shī shēngmen zhèngzài páiliàn yī bù xīn de shùxué huàjù ràng wǒmen cóng <jǐhé yuánběn > tán qǐ. – Teachers and students of the Department of Mathematics of East China Normal University are rehearsing a new mathematics drama „Let’s Start with <The Elements of Geometry>”.

哦振宁 | 什么风把你吹来了 | 快快快 | 你走路的时候你就可以问啊 | 并不是想知道你看了什么书 | 只是跟你寒暄一下行吧行吧 | 这是他们八年以来创作的 | 第八个话剧作品。Ó zhèn níng | shénme fēng bǎ nǐ chuī láile | kuài kuài kuài | nǐ zǒulù de shíhòu nǐ jiù kěyǐ wèn a | bìng bùshì xiǎng zhīdào nǐ kànle shénme shū | zhǐshì gēn nǐ hánxuān yīxià xíng ba xíng ba | zhè shì tāmen bā nián yǐlái chuàngzuò de | dì bā gè huàjù zuòpǐn. – Oh Zhenning | What wind brought you here | Hurry up | You can ask when you are walking | I don’t want to know what books you read | I just want to greet you, okay | This is the eight of them Created since 2008 | The eighth drama work.

主创人员大多是来自师范专业的学生创作话剧不是他们的专业人民教师。这是他们未来最有可能的角色。Zhǔchuàng rényuán dàduō shì láizì shīfàn zhuānyè de xuéshēng chuàngzuò huàjù bùshì tāmen de zhuānyè rénmín jiàoshī. Zhè shì tāmen wèilái zuì yǒu kěnéng de juésè.Most of the main creators are students from teachers’ majors who create plays, not their professional people’s teachers. This is their most likely role in the future.

可能以前我会觉得数学好难 | 但是当我接触了话剧之后 | 我会发现其实数学 | 可能对于那些数学家来说 | 也是很难的看到这些定理的时候 | 你会去联想到一代一代数学家 | 他们日以继夜地努力 | 来达到这么一个成就 | 那你会觉得他其实充满感情的 | 看到那边有一个人坐在沙滩椅上 | 然后我觉得现在的孩子们。

Kěnéng yǐqián wǒ huì juédé shùxué hǎo nán | dànshì dāng wǒ jiēchùle huàjù zhīhòu | wǒ huì fāxiàn qíshí shùxué | kěnéng duìyú nàxiē shùxué jiā lái shuō | yěshì hěn nán de kàn dào zhèxiē dìnglǐ de shíhòu | nǐ huì qù liánxiǎng dào yīdài yīdài shùxué jiā | tāmen rìyǐjìyè de nǔlì | lái dádào zhème yīgè chéngjiù | nà nǐ huì juédé tā qíshí chōngmǎn gǎnqíng de | kàn dào nà biān yǒuyī gèrén zuò zài shātān yǐ shàng | ránhòu wǒ juédé xiànzài de háizimen.

– Maybe I used to think mathematics was very difficult| But when I came into contact with the drama| I would find that in fact mathematics| Maybe for those mathematicians| It is also difficult to see these theorems| You will think of generation after generation of mathematics Home| They work day and night| to achieve such an achievement| Then you’ll think he’s actually full of emotion| See a guy over there sitting on a beach chair| And then I think the kids now.

至少有大部分没有感受到 | 数学它其实是有美的存在的 | 这也就是说我们 | 去做数学话剧的一个意义 | 数学话剧可能会给台下的一些观众 | 带来一种不一样的数学的体会 | 可能就会改变 | 他们的人生的努力方向。Zhìshǎo yǒu dà bùfèn méiyǒu gǎnshòu dào | shùxué tā qíshí shì yǒu měide cúnzài de | zhè yě jiùshì shuō wǒmen | qù zuò shùxué huàjù de yīgè yìyì | shùxué huàjù kěnéng huì gěi tái xià de yīxiē guānzhòng | dài lái yī zhǒng bù yīyàng de shùxué de tǐhuì | kěnéng jiù huì gǎibiàn | tāmen de rénshēng de nǔlì fāngxiàng. – At least most of them don’t feel | Mathematics actually has beauty | This means that we | do a meaning of mathematics drama | Mathematical drama may bring a different kind of mathematics to some audiences | experience | may change | the direction of their life efforts.

第二幕,第三场 | 在做了快四年的 | 数学话剧的工作中 | 最大的一个收获 | 就是让我确定了 | 我要做数学教育的这个方向。Dì èr mù, dì sān chǎng | zài zuòle kuài sì nián de | shùxué huàjù de gōngzuò zhōng | zuìdà de yīgè shōuhuò | jiùshì ràng wǒ quèdìngle | wǒ yào zuò shùxué jiàoyù de zhège fāngxiàng. – The second act, the third scene | I have been working on the mathematics drama for almost four years | The biggest gain | is to make me sure | I want to do this direction of mathematics education.

特别是你们数学家在发现它时没有参考物理世界你们数学家是凭空想象出来的。Tèbié shì nǐmen shùxué jiā zài fāxiàn tā shí méiyǒu cānkǎo wùlǐ shìjiè nǐmen shùxué jiā shì píngkōng xiǎngxiàng chūlái de. – Especially when you mathematicians discovered it without reference to the physical world you mathematicians imagined it out of thin air.

不不不不 | 我们不是凭空想象出来的 | 我觉得你的反驳不够强烈。不不不, 不对, 不对啊 | 所以我们想说 | 哪怕一个小孩子 | 他在观看这个话剧之后 | 他认识了一位数学家 | 或者说他知道有很多人 | 在为这个学科 | 在为这个社会 | 在为这个世界的发展 | 而做出努力的时候 | 其实我觉得这也就足够了。Bù bù bù bù | wǒmen bùshì píngkōng xiǎngxiàng chūlái de | wǒ juédé nǐ de fǎnbó bùgòu qiángliè. Bù bù bù, bùduì, bùduì a | suǒyǐ wǒmen xiǎng shuō | nǎpà yīgè xiǎo háizi | tā zài guānkàn zhège huàjù zhīhòu | tā rènshíle yī wèi shùxué jiā | huòzhě shuō tā zhīdào yǒu hěnduō rén | zài wèi zhège xuékē | zài wèi zhège shèhuì | zài wèi zhège shìjiè de fǎ zhǎn | ér zuò chū nǔlì de shíhòu | qíshí wǒ juédé zhè yě jiù zúgòule. – No no no no | We are not imagining it | I don’t think your rebuttal is strong enough. No, no, no, no | so we want to say | even a child | after watching this play | he met a mathematician | or he knew a lot of people | for this subject | for this Society | When making efforts for the development of this world | In fact, I think this is enough.

公演当天观众并不多 | 免费的数学话剧现场 | 显得有些太冷清了。或许在家长们的心中 | 花时间去接受一部话剧的熏陶 | 不是一个太划算的选择。Gōngyǎn dàngtiān guānzhòng bìng bù duō | miǎnfèi de shùxué huàjù xiànchǎng | xiǎndé yǒuxiē tài lěngqīngle. Huòxǔ zài jiāzhǎngmen de xīnzhōng | huā shíjiān qù jiēshòu yī bù huàjù de xūntáo | bùshì yīgè tài huásuàn de xuǎnzé. – There were not many audiences on the day of the performance | The free math drama scene | It seemed a little too deserted. Perhaps in the hearts of parents | taking time to accept the edification of a drama | is not a very cost-effective choice.

作为话剧创作题材 | 数学显得太不娱乐了 | 把数学家们的故事讲得引入入胜 | 确实很有难度。数学教育又何尝不是这样呢?Zuòwéi huàjù chuàngzuò tícái | shùxué xiǎndé tài bù yúlèle | bǎ shùxué jiāmen de gùshì jiǎng dé yǐnrù rù shèng | quèshí hěn yǒu nándù. Shùxué jiàoyù yòu hécháng bùshì zhèyàng ne? – As the subject of drama creation | Mathematics is too unentertaining | Telling the stories of mathematicians in a fascinating way | It is indeed very difficult. Isn’t that the case with mathematics education?

同学们的表演青涩稚嫩 | 但他们非常努力地讲了一个 | 关于数学的故事 | 塑造了一群数学家的形象 | 与此同时 | 他们他在塑造着未来的自己 | 以及未来的每一节数学课。Tóngxuémen de biǎoyǎn qīng sè zhìnèn | dàn tāmen fēicháng nǔlì de jiǎngle yīgè | guānyú shùxué de gùshì | sùzàole yīqún shùxué jiā de xíngxiàng | yǔ cǐ tóngshí | tāmen tā zài sùzàozhe wèilái de zìjǐ | yǐjí wèilái de měi yī jié shùxué kè. – The performances of the classmates were young and immature | but they worked very hard to tell a story | about mathematics | shaped the image of a group of mathematicians | at the same time | they were shaping the future self | class.

教育就是教会人们思考 | 但同时也要教会人们 | 对他们的思考负责 | 虽然这个说法 | 对几乎所有的课程都适用 | 但是它犬其适用于数学 | 因为数学是这样的一门学问 | 在其中一个小孩 | 能够确定他所得的结论是正确的 | 不是因为他的老师 | 或者教科书告诉是正确的 | 而是他的内在逻辑 | 能够让他确信 | 他的结论一定是正确的 | 这样的话 | 它培育人们的严谨的思考 | 培育人们的理性精神 | 培育人们的这种独立思考的意识 | 我想这个对教育来讲 | 是数学可以给教育提供的 | 非常重要的贡献。

Jiàoyù jiùshì jiàohuì rénmen sīkǎo | dàn tóngshí yě yào jiàohuì rénmen | duì tāmen de sīkǎo fùzé | suīrán zhège shuōfǎ | duì jīhū suǒyǒu de kèchéng dōu shìyòng | dànshì tā quǎn qí shìyòng yú shùxué | yīn wéi shùxué shì zhèyàng de yī mén xuéwèn | zài qízhōng yīgè xiǎohái | nénggòu quèdìng tā suǒdé de jiélùn shì zhèngquè de | bùshì yīnwèi tā de lǎoshī | huòzhě jiàokēshū gàosù shì zhèngquè de | ér shì tā de nèizài luójí | nénggòu ràng tā quèxìn | tā de jiélùn yīdìng shì zhèngquè de | zhèyàng dehuà | tā péiyù rénmen de yánjǐn de sīkǎo | péiyù rénmen de lǐxìng jīngshén | péiyù rénmen de zhè zhǒng dúlì sīkǎo de yìshí | wǒ xiǎng zhège duì jiàoyù lái jiǎng | shì shùxué kěyǐ gěi jiàoyù tígōng de | fēicháng zhòngyào de gòngxiàn.

– education is teaching people to think | but also teaching people | to be responsible for their thinking | although this statement | holds true for almost all courses | A child | can be sure that his conclusions are correct | not because of his teacher | or what the textbook says is correct | but his inner logic | can convince him | his conclusions must be correct | such | it Cultivate people’s rigorous thinking| Cultivate people’s rational spirit| Cultivate people’s consciousness of independent thinking| I think this is a very important contribution that mathematics can provide to education.

数学到底教会了我们什么呢?| 是数学知识 | 还是运用这些知识的方法 | 是解决各种难题的技巧 | 还是考出一个高分的能力。如果数学教育的根本目标 | 真的是要培养一个人的 | 理性思维能力 | 那么我们确实需要理性地反思一下 | 自己所受的数学教育 | 和这些品质到底有什么关系 | 我们到底学会了什么。。。Shùxué dàodǐ jiàohuìle wǒmen shénme ne?| Shì shùxué zhīshì | háishì yùnyòng zhèxiē zhīshì de fāngfǎ | shì jiějué gè zhǒng nántí de jìqiǎo | háishì kǎo chū yīgè gāo fēn de nénglì. Rúguǒ shùxué jiàoyù de gēnběn mùbiāo | zhēn de shì yào péiyǎng yīgè rén de | lǐxìng sīwéi nénglì | nàme wǒmen quèshí xūyào lǐxìng dì fǎnsī yīxià | zìjǐ suǒ shòu de shùxué jiàoyù | hé zhèxiē pǐnzhí dàodǐ yǒu shé me guānxì | wǒmen dàodǐ xuéhuìle shénme… – What does mathematics teach us? | Is it mathematical knowledge | Is it a method of applying this knowledge | Is it a skill to solve various problems | Is it the ability to get a high score. If the fundamental goal of mathematics education | really is to cultivate a person’s | rational thinking ability | then we really need to reflect rationally | what is the relationship between the mathematics education we have received and these qualities | what have we learned. . .

 

https://www.youtube.com/embed/q5ZJcrgLdUw?start=00

 

 

 

 

《被数学选中的人》第2集 Chosen By Mathematics EP2 数学家是如何工作的?他们经常研究与生活无关的东西到底有什么用呢?【CCTV纪录】Bèi shùxué xuǎnzhōng de rén dì 2 jí Chosen By Mathematics EP2 shùxué jiā shì rúhé gōngzuò de? Tāmen jīngcháng yánjiū yǔ shēnghuó wúguān de dōngxī dàodǐ yǒu shé me yòng ne?[CCTV jìlù] – The Chosen By Mathematics Episode 2 Chosen By Mathematics EP2 How do mathematicians work? What is the use of them often studying things that have nothing to do with life? 【CCTV record】

 

本期内容:一个新的数学成果被创造出来,很难在短时间内被转化为财富,谁也不知道哪一个数学理论会在什么时候成为主角。哥德巴赫猜想至今也没有被派上用场,他所关心的整数的各种性质,数学家们已经为此研究了2000多年,直到上世纪70年代,其中的某些理论才第一次被转化为具体的应用。

Běn qí nèiróng: Yīgè xīn de shùxué chéngguǒ bèi chuàngzào chūlái, hěn nán zài duǎn shíjiān nèi bèi zhuǎnhuà wéi cáifù, shéi yě bù zhīdào nǎ yīgè shùxué lǐlùn huì zài shénme shíhòu chéngwéi zhǔjiǎo.Gē dé bāhè cāixiǎng zhìjīn yě méiyǒu bèi pài shàng yòngchǎng, tāsuǒ guānxīn de zhěng shǔ de gè zhǒng xìngzhì, shùxué jiāmen yǐjīng wèi cǐ yánjiūle 2000 duōnián, zhídào shàng shìjì 70 niándài, qízhōng de mǒu xiē lǐlùn cái dì yī cì bèi zhuǎnhuà wéi jùtǐ de yìngyòng.

– Contents of this issue: A new mathematical achievement is created, and it is difficult to be converted into wealth in a short period of time. No one knows which mathematical theory will become the protagonist when. „Goldbach’s conjecture” has not been used so far. Mathematicians have been studying the properties of integers for more than 2,000 years. It was not until the 1970s that some of these theories were first used. into specific applications.

 

第二集

数学家工作

被数学选中的人

Dì èr jí shùxué jiā gōngzuò bèi shùxué xuǎnzhōng de rén

– Episode 2

mathematician work

chosen by mathematics

 

我们搜索到了一个很新的更重要的是完全看得懂的数学定理。

这就是四十二问题

数学家们经过六十五年的努力终于得出了这样一个等式。

这是三个十八位数字的三次方相加之和。

这个结构转化为数学定理是这样描述的:除了九 n±四型自然数外所有一百以内的自然数都能写成,三个整数的立方和.比如一可以写成这样,二可以写成这样,九十六可以写成这样。

Wǒmen sōusuǒ dàole yīgè hěn xīn de gèng zhòngyào de shì wánquán kàn dé dǒng de shùxué dìnglǐ. Zhè jiùshì sìshíèr wèntí”. Shùxué jiāmen jīngguò liùshíwǔ nián de nǔlì zhōngyú dé chūle zhèyàng yīgè děng shì. Zhè shì sān gè shíbā wèi shùzì de sāncì fāng xiàng jiā zhī hé. Zhège jiégòu zhuǎnhuà wéi shùxué dìnglǐ shì zhèyàng miáoshù de: Chúle jiǔ n±sì xíng zìránshù wài suǒyǒu yībǎi yǐnèi de zìránshù dōu néng xiěchéng, sān gè zhěng shǔ de lìfāng hé. Bǐrú yī kěyǐ xiěchéng zhèyàng, èr kěyǐ xiěchéng zhèyàng, jiǔshíliù kěyǐ xiěchéng zhèyàng.

– We searched for a very new and more importantly fully understandable mathematical theorem.

This is the „Forty-Two Questions”.

Mathematicians have finally arrived at such an equation after 65 years of hard work.

This is the sum of the cubes of three eighteen-digit numbers.

The transformation of this structure into a mathematical theorem is described as follows: all natural numbers within 100 except for the natural numbers of type 9n±4 can be written as the sum of the cubes of three integers. For example, one can be written like this, two can be written like this, ninety-six can be written like this.

 

四十二是一百以内最后一个没有找解的数字。它一度被誉成 宇宙的真理

说实话这样的数学新发现并没有震撼到我们这样的普通人最直接的感受反而是让世界上最聪明的大脑穷尽一生只是为了得出这样的结果实在是一种资源浪费。

Sìshíèr shì yībǎi yǐnèi zuìhòu yīgè méiyǒu zhǎo jiě de shùzì. Tā yīdù bèi yù chéng yǔzhòu de zhēnlǐ. Shuō shíhuà zhèyàng de shùxué xīn fāxiàn bìng méiyǒu zhènhàn dào wǒmen zhèyàng de pǔtōng rén zuì zhíjiē de gǎnshòu fǎn’ér shì ràng shìjiè shàng zuì cōngmíng de dànǎo qióngjìn yīshēng zhǐshì wèi liǎo dé chū zhèyàng de jiéguǒ shízài shì yī zhǒng zīyuán làngfèi.

– Forty-two is the last unsolved number within one hundred. It was once hailed as „the truth of the universe”.

To be honest, such new mathematical discoveries did not shock the most direct feelings of ordinary people like us. Instead, it is a waste of resources to let the smartest brain in the world spend its whole life just to get such a result.

这样的数学研究到底有什么用呢?你们到底在做什么?Zhèyàng de shùxué yánjiū dàodǐ yǒu shé me yòng ne? Nǐmen dàodǐ zài zuò shénme?  – What is the use of such mathematical research? What the hell are you doing?

数学家最难的去解释自己研究的东西。Shùxué jiā zuì nán de qù jiěshì zìjǐ yánjiū de dōngxī. – It is the hardest for mathematicians to explain what they are studying.

其本上有纸有笔有笔记本电脑就可以工作了。Qí běn shàng yǒu zhǐ yǒu bǐ yǒu bǐjìběn diànnǎo jiù kěyǐ gōngzuòle. – It can work with paper, pen and laptop.

几十亿人每个人都是个独立的个体对不对?

但是他有共性的东西大家都是两个眼睛一个鼻子一张嘴。

我就说数学家他善于从一个很表面上看来很复杂的一个东西。

他只要去找非常内在的一些简单的规律这个规律对谁都适用。

做数学是这样的他有一个目标他自己想上面要爬到一个山顶谁都没爬过的山。

你第一个去爬你不知道能不能爬上去。

Jǐ shí yì rén měi gèrén dōu shìgè dúlì de gètǐ duì bùduì? Dànshì tā yǒu gòngxìng de dōngxī dàjiā dōu shì liǎng gè yǎnjīng yīgè bízi yī zhāngzuǐ. Wǒ jiù shuō shùxué jiā tā shànyú cóng yīgè hěn biǎomiàn shàng kàn lái hěn fùzá de yīgè dōngxī. Tā zhǐyào qù zhǎo fēicháng nèizài de yīxiē jiǎndān de guīlǜ zhège guīlǜ duì shéi dōu shìyòng. Zuò shùxué shì zhèyàng de tā yǒu yīgè mùbiāo tā zìjǐ xiǎng shàngmiàn yào pá dào yīgè shāndǐng shéi dōu méi páguò de shān. Nǐ dì yī gè qù pá nǐ bù zhīdào néng bùnéng pá shàngqù.

– Each of billions of people is an individual, right?

But what he has in common is that everyone has two eyes, a nose and a mouth.

I would say that a mathematician is good at something that looks very complicated on the surface.

All he has to do is find some simple laws that are very internal. The laws apply to everyone.

Doing math is like this. He has a goal and he wants to climb to a mountain that no one has ever climbed.

You are the first to climb and you don’t know if you can climb up.

π 是圆周率是圆的周长和直径的比例。P shì yuánzhōulǜ shì yuán de zhōu cháng hé zhíjìng de bǐlì. – π is the ratio of the circumference to the diameter of a circle.

四千年前的古巴比伦文明 | 就对 π 进行了计算 | 当时的计算结果是三点一二五。Sìqiān nián qián de gǔ bābǐlún wénmíng | jiù duì p jìnxíngle jìsuàn | dāngshí de jìsuàn jiéguǒ shì sān diǎn yī’èrwǔ. – The Babylonian civilization 4,000 years ago | calculated π | The result was 3.125 at that time.

 古希腊时期 | 阿基米德用穷竭法来计算 π | 穷竭法的原理是 | 如果我们不能精确地计算圆的周长 | 那么我们就找一个和圆相似 | 周长又很好计算的图形 | 比如正方形来计算 | 当然正方形和圆形依然差别很大 | 但是如果我们增加边的数量 | 比如正五边形 | 就比正形更接边于园 | 正六边形就更接边一点 | 如此下来 | 正多边形的边数越多 | 就越接边于一个圆 | 所以如果把这些边的长度加起来 | 就趋边于圆的周长。

Gǔ xīlà shíqí | ā jī mǐ dé yòng qióngjié fǎ lái jìsuàn p | qióngjié fǎ de yuánlǐ shì | rúguǒ wǒmen bùnéng jīngquè de jìsuàn yuán de zhōu cháng | nàme wǒmen jiù zhǎo yīgè hé yuán xiāngsì | zhōu cháng yòu hěn hǎo jìsuàn de túxíng | bǐrú zhèngfāngxíng lái jìsuàn | dāngrán zhèngfāngxíng hé yuán xíng yīrán chābié hěn dà | dànshì rúguǒ wǒmen zēngjiā biān de shùliàng | bǐrú zhèng wǔ biān xíng | jiù bǐ zhèng xíng gèng jiē biān yú yuán | zhèngliù biān xíng jiù gèng jiē biān yīdiǎn | rúcǐ xiàlái | zhèng duōbiānxíng de biān shù yuè duō | jiù yuè jiē biān yú yīgè yuán | suǒyǐ rúguǒ bǎ zhèxiē biān de chángdù jiā qǐlái | jiù qū biān yú yuán de zhōu cháng.

– Ancient Greek Period | Archimedes used exhaustive method to calculate π | The principle of exhaustive method is | If we can’t calculate the circumference of a circle exactly| For example, to calculate with a square | Of course, a square and a circle are still very different | But if we increase the number of sides | For example, a regular pentagon | |The more sides of a regular polygon|, the more the sides are connected to a circle| So if you add up the lengths of these sides|, the sides tend to be the circumference of the circle.

阿基米德首先在圆里做了一个内接正四边形四条边的长度加起来就可以边似看作是圆的周长。Ā jī mǐ dé shǒuxiān zài yuán lǐ zuòle yīgè nèi jiē zhèng sìbiānxíng sìtiáo biān de chángdù jiā qǐlái jiù kěyǐ biān shì kàn zuò shì yuán de zhōu cháng. – Archimedes first made an inscribed regular quadrilateral in a circle. The lengths of the four sides can be added up, and the sides can be regarded as the circumference of the circle.

他巧妙地在圆之外 | 又做了一个外切正四边形 | 两个正四边形边长之和 | 除以园的直径 | 就是圆周率的上下边界 | 当然这个数值大粗略了 | 实际上阿基米德 | 是从正六边形开始计算 | 每次增加一倍的边数 | 也就是正十二边形 | 正二十四变形 | 不断增加 | 阿基米德一直算到九十六边形 | 得到的圆周率 | 是在三点一四零八到三点一四二九之间。

Tā qiǎomiào de zài yuán zhī wài | yòu zuòle yīgè wài qiē zhèng sìbiānxíng | liǎng gè zhèng sìbiānxíng biān zhǎng zhī hé | chú yǐ yuán de zhíjìng | jiùshì yuánzhōulǜ de shàngxià bian jiè | dāngrán zhège shùzhí dà cūlüèle | shíjì shang ā jī mǐ dé | shì cóng zhèngliù biān xíng kāishǐ jìsuàn | měi cì zēngjiā yī bèi de biān shù | yě jiùshì zhèng shíèr biān xíng | zhèng èrshísì biànxíng | bùduàn zēngjiā | ā jī mǐ dé yīzhí suàn dào jiǔshíliù biān xíng | dédào de yuánzhōulǜ | shì zài sān diǎn yīsì líng bā dào sān diǎn yīsìèrjiǔ zhī jiān.

– He cleverly made a circumscribed regular quadrilateral outside the circle | the sum of the side lengths of the two regular quadrilaterals | divided by the diameter of the circle | is the upper and lower boundaries of the pi | Of course, this value is rough | De | is calculated from the regular hexagon | the number of sides doubled each time | that is, the regular dodecagon | the regular twenty-four deformation | continues to increase | Archimedes has calculated until the ninety-six polygon | The pi| is between 3.1408 and 3.1429.

据说当罗马人攻进阿基米德的家乡叙拉古时阿基米德正在计算圆周率。 他怒斥一位走向他的罗马士兵说 不要弄乱我的圆。 结果这位莽撞的士兵挥剑刺死了阿基米德。

圆周率可能是这位伟大天才留给世间最后的财富。

Jùshuō dāng luómǎ rén gōng jìn ā jī mǐ dé de jiāxiāng xù lā gǔ shí ā jī mǐ dé zhèngzài jìsuàn yuánzhōulǜ. Tā nùchì yī wèi zǒuxiàng tā de luómǎ shìbīng shuō bùyào nòng luàn wǒ de yuán. Jiéguǒ zhè wèi mǎngzhuàng dí shìbīng huī jiàn cì sǐle ā jī mǐ dé. Yuánzhōulǜ kěnéng shì zhè wèi wěidà tiāncái liú gěi shìjiān zuìhòu de cáifù.

– It is said that Archimedes was calculating pi when the Romans attacked Syracuse, his hometown. He angrily rebuked a Roman soldier who approached him and said, „Don’t mess with my circle.” The reckless soldier stabbed Archimedes to death with his sword.

Pi may be the last treasure left to the world by this great genius.

四百多年后中国魏普时期的伟大数学家刘徽打破了圆周率计算的记录。

刘徽采用了和阿基米德类似的方法不过他没有用到外切多边形 | 只用不断增加 | 内接多边数的方法求解 | 这种方法叫割圆法 | 最终他计算出了 | 三千零七十二边形的周长 | 把圆周率精确到了小数点后四位 | 三点一四一六 | 接一千七百年前的科枝水平说 | 这已经是非常了不起的成就了。

四百多年后中国魏普时期的伟大数学家刘徽打破了圆周率计算的记录。

Sìbǎi duō nián hòu zhōngguó wèi pǔ shíqí de wěidà shùxué jiā liú huī dǎpòle yuánzhōulǜ jìsuàn de jìlù. Liú huī cǎiyòngle hé ā jī mǐ dé lèisì de fāngfǎ bùguò tā méiyǒu yòng dào wài qiē duōbiānxíng | zhǐ yòng bùduàn zēngjiā | nèi jiē duōbiān shǔ de fāngfǎ qiújiě | zhè zhǒng fāngfǎ jiào gē yuán fǎ | zuìzhōng tā jìsuàn chūle | sānqiān líng qīshíèr biān xíng de zhōu cháng | bǎ yuánzhōulǜ jīngquè dàole xiǎoshùdiǎn hòu sì wèi | sān diǎn yīsìyīliù | jiē yīqiān qībǎi nián qián de kē zhī shuǐpíng shuō | zhè yǐjīng shì fēicháng liǎobùqǐ de chéngjiùle.

– More than 400 years later, Liu Hui, a great mathematician during the Wei Pu period in China, broke the record of pi calculation.

Liu Hui used a method similar to that of Archimedes, but he did not use circumscribed polygons | he only used the method of increasing | the number of inscribed polygons to solve | This method is called the cut circle method | In the end he calculated | The perimeter of the zero-seventy-two polygons | Accurate the pi to four decimal places | 3.1416 | Connecting to the branch level of 1,700 years ago | This is already a very remarkable achievement.

二百年后南北朝时期的数学家祖冲之进一步用割圆法通过一万两千二百八十八边形得出了圆周率的新精准记录三点一四一五九二六 到 三点一四一五九二七 之间 | 祖冲之的这一纪录 | 一下子保特了边一千年 | 直到欧洲文艺复兴之后 | 人们又重新对圆周率的计算 | 充满了兴越 | 一六三零年奥地利天文学家格林伯格 | 计算出了 π 小数点后三十八位 | 九十年后圆周率精确到了小数点后一百位 | 时间进入二十世纪 | 计算机的发明迅猛提高了 | 数学家们的计算速度。

一九四九年美国数学家计算出小数点后两千三十七位。自此 π 尾巴 越来越长。到二零一九年圆周率已经被精确计算到小数点后三十一点四万亿位。

Èrbǎi nián hòu nánběicháo shíqí de shùxué jiā zǔchōngzhī jìnyībù yòng gē yuán fǎ tōngguò yī wàn liǎng qiān èrbǎi bāshíbā biān xíng dé chūle yuánzhōulǜ de xīn jīngzhǔn jìlù sān diǎn yīsìyīwǔjiǔ’èrliù dào sān diǎn yīsìyīwǔjiǔ’èrqī zhī jiān | zǔchōngzhī dì zhè yī jìlù | yīxià zi bǎo tèle biān yīqiān nián | zhídào ōuzhōu wényì fùxīng zhīhòu | rénmen yòu chóngxīn duì yuánzhōulǜ de jìsuàn | chōngmǎnle xìng yuè | yīliùsān líng nián àodìlì tiānwénxué jiā gélín bó gé | jìsuàn chūle p xiǎoshùdiǎn hòu sānshíbā wèi | jiǔshí nián hòu yuánzhōulǜ jīngquè dàole xiǎoshùdiǎn hòu yībǎi wèi | shíjiān jìnrù èrshí shìjì | jìsuànjī de fǎ míng xùnměng tígāole | shùxué jiāmen de jìsuàn sùdù. Yījiǔsìjiǔ nián měiguó shùxué jiā jìsuàn chū xiǎoshùdiǎn hòu liǎng qiān sānshíqī wèi. Zì cǐ p de wěibā yuè lái yuè zhǎng. Dào èr líng yījiǔ nián yuánzhōulǜ yǐjīng bèi jīngquè jìsuàn dào xiǎoshùdiǎn hòu sānshíyī diǎn sì wàn yì wèi.

– Two hundred years later, the mathematician Zu Chongzhi of the Southern and Northern Dynasties further used the cutting circle method to obtain a new accurate record of pi through 12,288 polygons: 3.1415926 to 3.141 Between 5927 | Zu Chongzhi’s record | All of a sudden it was kept for a thousand years | Until after the European Renaissance | People recalculated pi again | Full of excitement | Austrian astronomer in 1630 Greenberg | Calculated π to thirty-eight decimal places | Ninety years later, pi was accurate to one hundred decimal places | Time entered the twentieth century | The invention of the computer rapidly improved the calculation speed of mathematicians.

In 1949 American mathematicians calculated 2,370 decimal places. Since then, the „tail” of π has become longer and longer. By 2019, pi has been accurately calculated to 3.14 trillion decimal places.

π 还可以被继续计算下去因为它是一个无理数。它在小数点后的数字是无限且不循环出现的。P hái kěyǐ bèi jìxù jìsuàn xiàqù yīnwèi tā shì yīgè wúlǐshù. Tā zài xiǎoshùdiǎn hòu de shùzì shì wúxiàn qiě bù xúnhuán chūxiàn de. – π can still be calculated because it is an irrational number. Its digits after the decimal point are infinite and do not recur.

数学家们执着于计算一个不可能算到尽头的数字到底意义何在呢?Shùxué jiāmen zhízhuó yú jìsuàn yīgè bù kěnéng suàn dào jìntóu de shùzì dàodǐ yìyì hézài ne? – What is the point of mathematicians obsessing over an impossible number?

对于未知的天限追求是人类存在宇宙中的终极意义。

每一次数学知识体系的迭代都吸引着人们拿起更力的工具向 π 未知的终点继续靠近。

Duìyú wèizhī de tiān xiàn zhuīqiú shì rénlèi cúnzài yǔzhòu zhōng de zhōngjí yìyì. Měi yīcì shùxué zhīshì tǐxì de diédài dōu xīyǐnzhe rénmen ná qǐ gēng lì de gōngjù xiàng p wèizhī de zhōngdiǎn jìxù kàojìn.

– The pursuit of the unknown limit is the ultimate meaning of human existence in the universe.

Every iteration of the mathematical knowledge system attracts people to pick up more powerful tools and continue to approach the unknown end of π.

十八世纪 | 法国博物学家布丰 | 在意张白纸上 | 画满了等距离的平行线 | 再准备很多小针 | 针的长度 | 是平行线间距的一半 | 把针随意扔在纸上 | 然后计算与平行线相交的针的数量。

Shíbā shìjì | fàguó bówù xué jiā bù fēng | zàiyì zhāng bái zhǐ shàng | huà mǎnle děng jùlí de píngxíng xiàn | zài zhǔnbèi hěnduō xiǎo zhēn | zhēn de chángdù | shì píngxíng xiàn jiānjù de yībàn | bǎ zhēn suíyì rēng zài zhǐ shàng | ránhòu jìsuàn yǔ píngxíng xiàn xiàngjiāo de zhēn de shùliàng.

– Eighteenth Century | French Naturalist Buffon | Cares about a blank sheet of paper | Draws all the parallel lines at equal distances | Prepares many small needles | The length of the needles | Is half the distance between the parallel lines | | Then count the number of needles that intersect the parallel line.

神奇的是用这个数字去除针的总数结果竟然是 π 的近似值而且投掷次数越多得出的 π 值就越准确。

布丰投针实验是第一个用几何形式来表达概率问题的例子。

这原本是一个概率学的基础实验但冥冥之中却与圆周率发生了不可思议的关系。

π 的值到底意味着什么?

今天的数学家们仍对这个谜一样的数值 | 充满敬畏与憧憬。

Shénqí de shì yòng zhège shùzì qùchú zhēn de zǒngshù jiéguǒ jìngrán shì p de jìnsìzhí érqiě tóuzhí cìshù yuè duō dé chū de p zhí jiù yuè zhǔnquè. Bù fēng tóu zhēn shíyàn shì dì yīgè yòng jǐhé xíngshì lái biǎodá gàilǜ wèntí de lìzi. Zhè yuánběn shì yī gè gàilǜ xué de jīchǔ shíyàn dàn míng míng zhī zhōng què yǔ yuánzhōulǜ fā shēng liǎo bùkěsīyì de guānxì. P de zhí dàodǐ yìwèizhe shénme? Jīntiān de shùxué jiāmen réng duì zhège mí yīyàng de shùzhí | chōngmǎn jìngwèi yǔ chōngjǐng.

– The magic is that dividing the total number of pins by this number turns out to be an approximation of π and the more throws the more accurate the π value.

Buffon’s needle experiment was the first example of a probabilistic problem expressed in geometric form.

This was originally a basic experiment in probability, but it had an incredible relationship with pi.

What exactly does the value of pi mean?

Mathematicians today are still full of awe and longing for this enigmatic numerical value.

我们可以轻易画出的一个圆它就在那里。但因为 π 的存在一个普通的圆似乎包含着宇宙的规律。Wǒmen kěyǐ qīngyì huà chū de yīgè yuán tā jiù zài nàlǐ. Dàn yīnwèi p de cúnzài yīgè pǔtōng de yuán sìhū bāohánzhe yǔzhòu de guīlǜ.

– A circle we can easily draw and it’s there.But because of the existence of π, an ordinary circle seems to contain the laws of the universe.

您可以想象一下像圆。

圆是有不同的圆。

有大的圆有小的圆有千千万万的圆。

但是不管是哪个圆它的圆周跟它的直径一定满足刚才你讲的那个圆周率的关系那种比例关系。

这就是一件非常奇妙的事情。

Nín kěyǐ xiǎngxiàng yīxià xiàng yuán. Yuán shì yǒu bùtóng de yuán. Yǒu dà de yuán yǒu xiǎo de yuán yǒu qiān qiān wàn wàn de yuán. Dànshì bùguǎn shì nǎge yuán tā de yuánzhōu gēn tā de zhíjìng yīdìng mǎnzú gāngcái nǐ jiǎng dì nàgè yuánzhōulǜ de guānxì nà zhǒng bǐlì guānxì. Zhè jiùshì yī jiàn fēicháng qímiào de shìqíng.

– You can imagine like a circle.

Circles are different circles.

There are big circles, small circles, and thousands of circles.

But no matter which circle it is, its circumference and its diameter must satisfy the proportional relationship of the pi ratio you just mentioned.

This is a very wonderful thing.

所以它会让让一切变得简单也就是说我们不是看到一百个点就是一百个点。它可能来自于一个规则所以我可能只需要站在光束的源头就可以覆盖到得大的区域。Suǒyǐ tā huì ràng ràng yīqiè biàn dé jiǎndān yě jiùshì shuō wǒmen bùshì kàn dào yībǎi gè diǎn jiùshì yībǎi gè diǎn. Tā kěnéng láizì yú yīgè guīzé suǒyǐ wǒ kěnéng zhǐ xūyào zhàn zài guāngshù de yuántóu jiù kěyǐ fùgài dào dé dà de qūyù. – So it will make it easy to say that we either see a hundred dots or a hundred dots. It might come from a rule so I might just have to stand at the source of the beam to cover a large area.

要想完全理解数学家所做的工作并不容易。他们试图用数学逻辑把复杂世界的确定性结构分析出来找到那些隐藏在表象背后的底层规律帮助人们从迷茫中看了道路从混乱中找到了秩序。Yào xiǎng wánquán lǐ xiè shùxué jiā suǒ zuò de gōngzuò bìng bù róngyì. Tāmen shìtú yòng shùxué luójí bǎ fùzá shìjiè dí quèdìng xìng jiégòu fēnxī chūlái zhǎodào nàxiē yǐncáng zài biǎoxiàng bèihòu de dǐcéng guīlǜ bāngzhù rénmen cóng mímáng zhòng kànle dàolù cóng hǔnluàn zhōng zhǎodàole zhìxù. – It’s not easy to fully understand what mathematicians do. They try to use mathematical logic to analyze the deterministic structure of the complex world and find the underlying laws hidden behind the appearance, helping people to see the road from confusion and find order from chaos.

他们以一种特有的动力方式往返穿梭于数学世界现实世界以及我们的感官世界。Tāmen yǐ yī zhǒng tèyǒu de dònglì fāngshì wǎngfǎn chuānsuō yú shùxué shìjiè xiànshí shìjiè yǐjí wǒmen de gǎnguān shìjiè. – They travel back and forth between the real world of mathematics and the world of our senses in a peculiarly dynamic way.

有一些原始的问题就是人们在现实生活中提出来的它就是迫切需要解决的实际问题。Yǒu yīxiē yuánshǐ de wèntí jiùshì rénmen zài xiànshí shēnghuó zhōng tí chūlái de tā jiùshì pòqiè xūyào jiějué de shíjì wèntí. – There are some original problems that people raise in real life, which are practical problems that need to be solved urgently.

它就是迫切需要解决的实际问题。

经过了近两千多年的所谓数学发展的历程然后现代的数学已经变得非常复杂了 | 它已经不是再这么简单地 | 去处理说我们日常生活中 | 能遇到的一些生活琐碎的 | 一些数学问题 | 所以对于这些老百姓来说 | 他们可能感觉说数学很高深 | 感觉数学对他们生活 | 日常生活的用处并不大 | 我们不太能否认这种感受 | 这的确就是现实。

Tā jiùshì pòqiè xūyào jiějué de shíjì wèntí. Jīng guò liǎo jìn liǎng qiān duō nián de suǒwèi shùxué fāzhǎn de lìchéng ránhòu xiàndài de shùxué yǐjīng biàn dé fēicháng fùzále | tā yǐjīng bùshì zài zhème jiǎndān de | qù chǔlǐ shuō wǒmen rìcháng shēnghuó zhōng | néng yù dào de yīxiē shēnghuó suǒsuì de | yīxiē shùxué wèntí | suǒyǐ duìyú zhèxiē lǎobǎixìng lái shuō | tāmen kěnéng gǎnjué shuō shùxué hěn gāoshēn | gǎnjué shùxué duì tāmen shēnghuó | rìcháng shēnghuó de yòngchù bìng bù dà | wǒmen bù tài néng fǒurèn zhè zhǒng gǎnshòu | zhè díquè jiùshì xiànshí.

– It is a practical problem that urgently needs to be solved.

After nearly two thousand years of so-called mathematics development, modern mathematics has become very complicated | it is no longer so simple | to deal with some trivial things that we can encounter in our daily life | some Mathematical problems | So for these ordinary people | They may feel that mathematics is very advanced | Feel that mathematics is of little use in their daily life | We cannot deny this feeling | This is indeed the reality.

它就是一个高级的存在 | 他就是在你的 | 生理和心理极限之外的一种存在 | 它必须要有。Tā jiùshì yīgè gāojí de cúnzài | tā jiùshì zài nǐ de | shēnglǐ hé xīnlǐ jíxiàn zhī wài de yī zhǒng cúnzài | tā bìxū yào yǒu. – It is a higher being | it is a being that is beyond your | physical and mental limits | it has to be.

数学家的研究成果和人们的实际生活往往相距甚运但我们的生活的确是在数学的推动下走到今天的。Shùxué jiā de yánjiū chéngguǒ hé rénmen de shíjì shēnghuó wǎngwǎng xiāngjù shén yùn dàn wǒmen de shēnghuó díquè shì zài shùxué de tuīdòng xià zǒu dào jīntiān de. – The research results of mathematicians and people’s actual life are often far away, but our life is indeed driven by mathematics to today.

上世纪七十年代美国物理学家科马克在积分几何的基础上 | 建立起了人体不同组织 | 对 X 射线吸收量的计算分式。Shàng shìjì qīshí niándài měiguó wùlǐ xué jiā kē mǎkè zài jīfēn jǐhé de jīchǔ shàng | jiànlì qǐle réntǐ bùtóng zǔzhī | duì X shèxiàn xīshōu liàng de jìsuàn fēn shì. – In the 1970s, American physicist Cormack established a formula for calculating the absorption of X-rays by different tissues of the human body on the basis of integral geometry.

在这项数学成果的支持下一九七一年英国电气工程师豪斯菲尔德发明了第一台 CT (计算机体层成像) 扫描仪成全人类的健康保驾护航。Zài zhè xiàng shùxué chéngguǒ de zhīchí xià yījiǔqīyī nián yīngguó diànqì gōngchéngshī háo sī fēi’ěrdé fāmíngliǎo dì yī tái CT (jìsuànjī tǐ céng chéngxiàng) sǎomiáo yí chéngquán rénlèi de jiànkāng bǎojià hùháng. – With the support of this mathematical achievement, British electrical engineer Housefield invented the first CT (computed tomography) scanner in 1971 to escort the health of all human beings.

数学里面更多的情况是由于它自身的理论发展需要而推进的一些研究比如说经常提到的 哥德巴赫猜想Shùxué lǐmiàn gèng duō de qíngkuàng shì yóuyú tā zìshēn de lǐlùn fāzhǎn xūyào ér tuījìn de yīxiē yánjiū bǐrú shuō jīngcháng tí dào de gē dé bāhè cāixiǎng. – In mathematics, there are more researches that are promoted due to its own theoretical development needs, such as the often mentioned „Goldbach conjecture”.

哥德巴赫猜想 大概是中国人最熟知的一个高深的数学问题。Gē dé bāhè cāixiǎng dàgài shì zhōngguó rén zuì shúzhī de yīgè gāoshēn de shùxué wèntí. – „Goldbach’s conjecture” is probably the most profound mathematical problem that Chinese people are familiar with.

一七四二年普鲁士数学家哥德巴赫在写给数学泰斗欧拉的信中提出了一个自己偶然想到的关于素的发现。Yīqīsìèr nián pǔlǔshì shùxué jiā gē dé bāhè zài xiě gěi shùxué tàidǒu ōu lā de xìn zhōng tíchūle yīgè zìjǐ ǒurán xiǎngdào de guānyú sù de fǎ xiàn. – In 1742, the Prussian mathematician Goldbach made a discovery about primes that he stumbled upon in a letter to Euler.

所谓素数简单说就是不能被除了一 | 和自身之外的数整除的数比如三,五,七 等而九可以被三整除,十五可以被三合五整除。这些就不是素数。Suǒwèi sùshù jiǎndān shuō jiùshì bùnéng bèi chúle yī | hé zìshēn zhī wài de shù zhěngchú de shù bǐrú sān, wǔ, qī děng ér jiǔ kěyǐ bèi sān zhěngchú, shíwǔ kěyǐ bèi sān hé wǔ zhěngchú. Zhèxiē jiù bùshì sùshù. – The so-called prime numbers are simply numbers that are not divisible by numbers other than one | and itself, such as three, five, seven, etc., while nine is divisible by three, and fifteen is divisible by three-to-five. These are not prime numbers.

哥德巴赫猜想任何一个大于二的偶数都可以写成一个素数加上另外一个素数的和。Gē dé bāhè cāixiǎng rènhé yīgè dàyú èr de ǒushù dōu kěyǐ xiěchéng yīgè sùshù jiā shàng lìngwài yīgè sù shǔ de hé. – Goldbach conjectured that any even number greater than two can be written as the sum of a prime number plus another prime number.

 比如八可以写成三加五,三合五都是素数。十可以写成三加七,三和七也都是素数。它也被今天的人们简称为一加一 的问题。

这里的 代表一个素数这个歌德巴赫不知道怎样突发奇想做出的猜想却难倒了欧拉也难倒了从十八世纪到今天的无数数学家近三百年间。

数学家们证明了”九加九”,二加三 再到 一加五一加四 一加三,但一加一 仍然遥不可及。

Bǐrú bā kěyǐ xiěchéng sān jiā wǔ, sān hé wǔ dōu shì sùshù. Shí kěyǐ xiěchéng sān jiā qī, sān hé qī yě dū shì sùshù. Tā yě bèi jīntiān de rénmen jiǎnchēng wèi yī jiā yī de wèntí. Zhèlǐ de dàibiǎo yīgè sùshù zhège gēdé bāhè bù zhīdào zěnyàng tú fā qíxiǎng zuò chū de cāixiǎng què nán dǎo le ōu lā yě nán dǎo le cóng shíbā shìjì dào jīntiān de wúshù shùxué jiā jìn sānbǎi nián jiān. Shùxué jiāmen zhèngmíngliǎo”jiǔ jiā jiǔ”,“èr jiā sān zài dào yī jiā wǔ,yī jiā sì” yī jiā sān, dàn yī jiā yī réngrán yáo bùkě jí.

– For example, eight can be written as three plus five, and three plus five are prime numbers. Ten can be written as three plus seven, and three and seven are also prime numbers. It is also referred to simply as the „one plus one” problem by people today.

The „one” here stands for a prime number, a conjecture that Goldbach did not know how to make on a whim, but it stumped Euler and stumped countless mathematicians from the eighteenth century to today for nearly three hundred years.

Mathematicians have proven „nine plus nine”, „two plus three” to „one plus five”, „one plus four” and „one plus three”, but „one plus one” is still out of reach.

 一九六六年中国数学家陈景润取得了重大突破。他证明了 一加二Yījiǔliùliù nián zhōngguó shùxué jiā chénjǐngrùn qǔdéle zhòngdà túpò. Tā zhèngmíngliǎo yī jiā èr. – In 1966, Chinese mathematician Chen Jingrun made a major breakthrough. He proved „one plus two”.

 它可以写成任何一个大于六的偶数。可以写成一个素数加上另外两个家伙乘起来。

比方说二十二可以写成三乘以五,这是两个素数对吧三乘五等于十五再加一个七了。

Tā kěyǐ xiěchéng rènhé yīgè dàyú liù de ǒushù. Kěyǐ xiěchéng yīgè sùshù jiā shàng lìngwài liǎng gè jiāhuo chéng qǐlái. Bǐfāng shuō èrshíèr kěyǐ xiěchéng sān chéng yǐ wǔ, zhè shì liǎng gè sùshù duì ba sān chéng wǔ děngyú shíwǔ zài jiā yīgè qīle.

– It can be written as any even number greater than six. Can be written as a prime plus two other guys multiplied together.

For example, twenty-two can be written as three times five, which is two prime numbers, so three times five equals fifteen plus seven.

二十二也可以写成十一架十一,就是两个一加一对不对?

所以一加一就是一个素数加一个素数。

Èrshíèr yě kěyǐ xiěchéng shíyī jià shíyī, jiùshì liǎng gè yī jiā yī duì bùduì? Suǒyǐ yī jiā yī jiùshì yīgè sùshù jiā yīgè sùshù.

– Twenty-two can also be written as eleven and eleven, which is two one plus one pair, right?

So one plus one is a prime plus a prime.

哥德巴赫猜想 就说明一个鲜明的特点 | 它说起来很简单 | 小学生都能听懂 | 但是做起来了 | 世界上最伟大的数学家 | 就这是个题目 | 哥德巴赫猜想 到目前为止不是没解决。Gē dé bāhè cāixiǎng jiù shuōmíng yīgè xiānmíng de tèdiǎn | tā shuō qǐlái hěn jiǎndān | xiǎoxuéshēng dōu néng tīng dǒng | dànshì zuò qǐláile | shìjiè shàng zuì wěidà de shùxué jiā | jiù zhè shìgè tímù | gē dé bāhè cāixiǎng dào mùqián wéizhǐ bùshì méi jiějué. – „Goldbach’s conjecture” shows a distinctive feature | it’s easy to say | elementary school children can understand | but it’s done | Not unresolved so far.

老百姓觉得这个东西:一个数能不能拆成两个东西相乘,或者相加有什么用很多数学的问题?Lǎobǎixìng juédé zhège dōngxī: Yīgè shù néng bùnéng chāi chéng liǎng gè dōngxī xiāng chéng, huòzhě xiàng jiā yǒu shé me yòng hěnduō shùxué de wèntí? – The common people think this thing: Can a number be divided into two things to multiply, or what is the problem of adding a lot of mathematics?

表面上看来可能是没用 | 比方说 哥德巴赫猜想 | 现在我们不知道 | 它将来证完以后会有什么用 | 但是也可能会有很大的用 | 因为数学家他做的时候 | 他并不是考虑 | 这个东西有什么用才去做 | 他还是觉得这个东西很神奇。

Biǎomiàn shàng kàn lái kěnéng shì méi yòng | bǐfāng shuō gē dé bāhè cāixiǎng | xiànzài wǒmen bù zhīdào | tā jiānglái zhèng wán yǐhòu huì yǒu shé me yòng | dànshì yě kěnéng huì yǒu hěn dà de yòng | yīn wéi shùxué jiā tā zuò de shíhòu | tā bìng bùshì kǎolǜ | zhège dōngxī yǒu shé me yòng cái qù zuò | tā háishì juédé zhège dōngxī hěn shénqí.

– It may be useless on the surface | For example, „Goldbach’s conjecture” | Now we don’t know | What use it will be in the future | But it may be of great use | Because when the mathematician he did | He didn’t think about | what is the use of this thing to do it | He still thinks this thing is amazing.

提出猜想是非常重要的数学发展的一个手段。

当我们提出猜想之后我们才有好奇心说去探索这个猜想到底对不对 | 当没有问题 | 当没有猜想的时候 | 数学是很难以发展的 | 因为引领数学推动的动力 | 就是我们讲的好奇 | 对于数学世界的好奇。

Tíchū cāixiǎng shì fēicháng zhòngyào de shùxué fāzhǎn de yīgè shǒuduàn. Dāng wǒmen tíchū cāixiǎng zhīhòu wǒmen cái yǒu hàoqí xīn shuō qù tànsuǒ zhège cāixiǎng dàodǐ duì bùduì | dāng méiyǒu wèntí | dāng méiyǒu cāixiǎng de shíhòu | shùxué shì hěn nányǐ fāzhǎn de | yīnwèi yǐnlǐng shùxué tuīdòng de dònglì | jiùshì wǒmen jiǎng de hàoqí | duìyú shùxué shìjiè de hàoqí.

– Making conjectures is a very important means of mathematical development.

When we make a conjecture, we are curious to explore whether the conjecture is right or not | When there is no problem | When there is no conjecture | Mathematics is difficult to develop | Because the driving force that leads mathematics | is what we call curiosity | For The curiosity of the mathematical world.

哥德巴赫猜想 更具传奇色彩的是费马大定理Bǐ gē dé bāhè cāixiǎng gèng jù chuánqí sècǎi de shì fèi mǎ dà dìnglǐ. – More legendary than the „Goldbach Conjecture” is „Fermat’s Last Theorem”.

费马是十七世纪一位天才的业余数学家。他的真实身份是一位律师。Fèi mǎ shì shíqī shìjì yī wèi tiāncái de yèyú shùxué jiā. Tā de zhēnshí shēnfèn shì yī wèi lǜshī. – Fermat was a talented amateur mathematician in the seventeenth century. His real identity is a lawyer.

脱下律师袍后他的业余时间全部倾注在数学研究上。

费马推导出的很多定理都被证明是正确的但他有一个习惯逃避推导过程。

他的手稿中经常出现这样的话 我可以证明这个结论但我现在必须去喂猫了 或者 我要去洗头了。

Tuō xià lǜshī páo hòu tā de yèyú shíjiān quánbù qīngzhù zài shùxué yánjiū shàng. Fèi mǎ tuīdǎo chū de hěnduō dìnglǐ dōu bèi zhèngmíng shì zhèngquè de dàn tā yǒu yīgè xíguàn táobì tuīdǎo guòchéng. Tā de shǒugǎo zhōng jīngcháng chūxiàn zhèyàng dehuà wǒ kěyǐ zhèngmíng zhège jiélùn dàn wǒ xiànzài bìxū qù wèi māole huòzhě wǒ yào qù xǐ tóule.

– After taking off his lawyer’s robe, he devoted all his spare time to mathematical research.

Many of the theorems Fermat derived were proven correct but he had a habit of escaping the derivation process.

Frequently in his manuscripts the words „I can prove this but I have to feed the cat now” or „I am going to wash my hair.”

 一六三七年费马在阅读古希腊数学家丢番图的名作 《算术》时老毛病又犯了。Yīliùsānqī nián fèi mǎ zài yuèdú gǔ xīlà shùxué jiā diū fān tú de míngzuò suànshù” shí lǎo máobìng yòu fànle. – In 1637 Fermat relapsed when he was reading the masterpiece „Arithmetic” by the ancient Greek mathematician Diophantus.

他在书页空白处写下了这样一个困扰了人类今后三百六十年的定理:X 的 n 次方加 Y 的 n 次方等于 Z 的 n 次方当 n 大于二时没有正整数

让人们抓狂的是费马接下来写道:我确信已经发现了一种美妙的证法可惜这里空白的地方大小写不下。

Tā zài shūyè kòngbái chù xiě xiàle zhèyàng yīgè kùnrǎole rénlèi jīnhòu sānbǎi liùshí nián de dìnglǐ:X de n cì fāng jiā Y de n cì fāng děngyú Z de n cì fāng dāng n dàyú èr shí méiyǒu zhèng zhěngshù”. Ràng rénmen zhuā kuáng de shì fèi mǎ jiē xiàlái xiě dào:Wǒ quèxìn yǐjīng fāxiànle yī zhǒng měimiào de zhèng fǎ kěxí zhèlǐ kòngbái dì dìfāng dàxiǎo xiě bùxià.

– He wrote in the margin of the book such a theorem that has troubled mankind for the next 360 years: „X to the nth power plus Y to the nth power is equal to Z to the nth power. When n is greater than two, there is no positive integer”.

What drives people crazy is that Fermat goes on to write: „I’m sure a wonderful proof has been discovered, but the blank space here is not capitalized.”

在这个公式中如果 n 等于二的话 是有正整数解的比如三的二次方加四的二次方等于五的二次方。

但是费马断定如果这个 n 大于二的话这个方程就不会有正整数解。这就是 费马大定理

Zài zhège gōngshì zhōng rúguǒ n děngyú èr dehuà shì yǒu zhèng zhěngshù jiě de bǐrú sān de èr cì fāng jiā sì de èr cì fāng děngyú wǔ de èr cì fāng. Dànshì fèi mǎ duàndìng rúguǒ zhège n dàyú èr dehuà zhège fāngchéng jiù bù huì yǒu zhèng zhěngshù jiě. Zhè jiùshì fèi mǎ dà dìnglǐ.

– In this formula, if n is equal to two, then there is a positive integer solution, such as the power of three plus the power of four equals the power of five.

But Fermat concluded that if this n was greater than two the equation would not have a positive integer solution. This is „Fermat’s Last Theorem”.

这样一个简单到初中生都能理解 | 又被费马轻描淡写 | 省略了推导过程的定理 | 成为了一个之后三百年间 | 数学家兴奋沮丧失落的魔咒。Zhèyàng yīgè jiǎndān dào chūzhōng shēng dōu néng lǐjiě | yòu bèi fèi mǎ qīngmiáodànxiě | shěnglüèle tuīdǎo guòchéng de dìnglǐ | chéngwéile yīgè zhīhòu sānbǎi nián jiān | shùxué jiā xīngfèn jǔsàng shīluò de mó zhòu. – Such a simple enough to be understood by junior high school students | It was downplayed by Fermat again | The theorem that omits the derivation process | It has become a curse for mathematicians in the next three hundred years | excitement, frustration and loss.

 同时代最著名的数学家欧拉首先尝试他证明了 n 等于三时费马大定理 成立但仅仅到此为止。Tóngshí dài zuì zhùmíng de shùxué jiā ōu lā shǒuxiān chángshì tā zhèngmíngliǎo n děngyú sān shí fèi mǎ dà dìnglǐ chénglì dàn jǐnjǐn dào cǐ wéizhǐ. – Euler, the most famous mathematician of his time, first tried his proof that „Fermat’s Last Theorem” holds when n is equal to three, but only so far.

十九世纪初法国女数学家索菲·热尔曼提出用一类素数的集合而不是无休止地证明每一个数字的新证法。

在热尔曼素数提出之后数学家们先后证明了 n 等于五和七的状况下定理成立。

之后法国数学家拉梅和柯西同时宣布自己证明了 费马大定理

不过他们还没有召开发布会 | 就被一位德国数学家库默尔 | 发现了致命漏洞 | 库默尔认为 | 当时的数学工具 | 无法证明 费马大定理 是否成立这下全世界数学界被浇了一盆冷水。

Shíjiǔ shìjì chū fàguó nǚ shùxué jiā suǒ fēi·rè ěr màn tíchū yòng yī lèi sù shǔ de jíhé ér bùshì wú xiūzhǐ dì zhèngmíng měi yīgè shùzì de xīn zhèng fǎ. Zài rè ěr màn sùshù tíchū zhīhòu shùxué jiāmen xiānhòu zhèngmíngliǎo n děngyú wǔ hé qī de zhuàngkuàng xià dìnglǐ chénglì. Zhīhòu fàguó shùxué jiā lā méi hé kē xī tóngshí xuānbù zìjǐ zhèngmíngliǎo fèi mǎ dà dìnglǐ. Bùguò tāmen hái méiyǒu zhàokāi fābù huì | jiù bèi yī wèi déguó shùxué jiā kù mò ěr | fāxiànle zhìmìng lòudòng | kù mò ěr rènwéi | dāngshí de shùxué gōngjù | wúfǎ zhèngmíng fèi mǎ dà dìnglǐ shìfǒu chénglì zhè xià quán shìjiè shùxué jiè bèi jiāole yī pén lěngshuǐ.

– At the beginning of the nineteenth century, the French female mathematician Sophie Germain proposed a new proof method that uses a set of prime numbers instead of endlessly proving each number.

After the Germain primes were proposed, mathematicians successively proved that the theorem holds when n is equal to five and seven.

Later, French mathematicians Lame and Cauchy announced that they had proved „Fermat’s Last Theorem” at the same time.

But they haven’t held a press conference yet | they were discovered by a German mathematician Kummer | A fatal loophole | Kummer thinks | Mathematical tools at that time | Was poured a basin of cold water.

真到二十世纪初一天德国实业家兼数学爱好者保罗 · 沃尔夫斯凯尔因为失恋而决定自杀 | 他确定了一个自杀的时间 | 然后以在图书馆里 | 读数学书的方式等待死亡。

恰好他看到了库默尔解释 费马大定理 无法证明论文。

Zhēn dào èrshí shìjì chū yītiān déguó shíyè jiā jiān shùxué àihào zhě bǎoluó· wò ēr fū sī kǎi ěr yīnwèi shīliàn ér juédìng zìshā | tā quèdìngle yīgè zìshā de shíjiān | ránhòu yǐ zài túshū guǎn lǐ | dú shùxué shū de fāngshì děngdài sǐwáng. Qiàhǎo tā kàn dàole kù mò ěr jiěshì fèi mǎ dà dìnglǐ wúfǎ zhèngmíng lùnwén.

– One day at the beginning of the twentieth century, German industrialist and mathematics enthusiast Paul Wolfskell decided to commit suicide because of a broken love | He set a time for suicide | Then he waited for death by reading mathematics books in the library .

He happened to see Kummer explaining that „Fermat’s Last Theorem” could not prove the paper.

沃尔夫斯凯尔突然发现库默尔的论证中也有一个关键漏洞。

这意味着 费马大定理 不一定是不可证明的。

沃尔夫斯凯尔兴奋异常开始埋头研究这一下就错过了自杀的时间。

Wò ēr fū sī kǎi ěr túrán fāxiàn kù mò ěr dì lùnzhèng zhōng yěyǒu yīgè guānjiàn lòudòng. Zhè yìwèizhe fèi mǎ dà dìnglǐ bù yīdìng shì bùkě zhèngmíng de. Wò ēr fū sī kǎi ěr xīngfèn yìcháng kāishǐ máitóu yánjiū zhè yīxià jiù cuòguòle zìshā de shíjiān.

– Wolfscale suddenly discovered a key hole in Kummer’s argument, too.

This means that „Fermat’s Last Theorem” is not necessarily unprovable.

Wolfskehl was so excited that he began to immerse himself in research and missed the time to commit suicide.

为了对 费马大定理 这位 救命恩人 表示感谢沃尔夫斯凯尔设立了一笔十万马克的巨奖用以奖励证明定理的那个人。

Wèile duì fèi mǎ dà dìnglǐ zhè wèi jiùmìng ēnrén biǎoshì gǎnxiè wò ēr fū sī kǎi ěr shèlìle yī bǐ shí wàn mǎkè de jù jiǎng yòng yǐ jiǎnglì zhèngmíng dìnglǐ dì nàgè rén.

– In order to thank the „Savior” of „Fermat’s Last Theorem”, Wolfskehl has set up a huge prize of 100,000 marks to reward the person who proves the theorem.

几十年过去了 | 计算机的发明大大提高了运算能力 | 人们已经证明 | 在 n 小于四千一百万的情况下 | 定理都是成立的 | 但是四千一百万零一呢?

Jǐ shí nián guòqùle | jìsuànjī de fǎ míng dàdà tígāole yùnsuàn nénglì | rénmen yǐjīng zhèngmíng | zài n xiǎoyú sìqiān yībǎi wàn de qíngkuàng xià | dìnglǐ dōu shì chénglì de | dànshì sìqiān yībǎi wàn líng yī ne?

– Decades have passed | the invention of the computer has greatly improved computing power | it has been proved | in the case of n less than 41 million | the theorem is true | but what about 41 million and 1?

费马大定理 历经三百年仍然是一个看不到尽头的黑洞。Fèi mǎ dà dìnglǐ lìjīng sānbǎi nián réngrán shì yīgè kàn bù dào jìntóu de hēidòng. – „Fermat’s Last Theorem” remains a black hole with no end in sight after three hundred years.

一九五五年日本数学家谷山丰和志村五郎公布了一个猜想每个椭圆方程者可以用模形式表达出来 | 之后德国数学家弗赖把 费马大定理 | 和谷山-志村猜想联系了起来 | 也就是只要证明了谷山-志村猜想 | 就可以证明 费马大定理 的 | 解决方向 | 一九九五年 | 英国数学家怀尔斯 | 最终证明了 费马大定理 成立 | 这个困扰了人类最聪明大脑 | 长达三百六十年的问题终于被解决了。

Yījiǔwǔwǔ nián rìběn shùxué jiā gǔshān fēng hé zhìcūn wǔláng gōngbùle yīgè cāixiǎng měi gè tuǒyuán fāngchéng zhě kěyǐ yòng mó xíngshì biǎodá chūlái | zhīhòu déguó shùxué jiā fú lài bǎ fèi mǎ dà dìnglǐ | hé gǔshān-zhìcūn cāixiǎng liánxìle qǐlái | yě jiùshì zhǐyào zhèngmíngliǎo gǔshān-zhìcūn cāixiǎng | jiù kěyǐ zhèngmíng fèi mǎ dà dìnglǐ de | jiějué fāngxiàng | yījiǔjiǔwǔ nián | yīngguó shùxué jiā huái ěr sī | zuìzhōng zhèngmíngliǎo fèi mǎ dà dìnglǐ chénglì | zhège kùnrǎole rénlèi zuì cōngmíng dànǎo | zhǎng dá sānbǎi liùshí nián de wèntí zhōngyú bèi jiějuéle.

– In 1955, Japanese mathematicians Taniyama Feng and Shimura Goro published a conjecture that every ellipse equation can be expressed in modular form | After that, German mathematician Frey linked „Fermat’s Last Theorem” with the Taniyama-Shimura conjecture Get up| That is, as long as the Taniyama-Shimura conjecture is proved|, the solution direction of „Fermat’s Last Theorem” can be proved| 1995| British mathematician Wiles | This 360-year-old problem that has plagued the smartest brains of mankind has finally been solved.

然而这样一个跌宕起伏 | 绵延三百年的证明过程 | 给人类留下了什么呢?Rán’ér zhèyàng yīgè diēdàng qǐfú | miányán sānbǎi nián de zhèngmíng guòchéng | jǐ rénlèi liú xiàle shénme ne? – However, such an ups and downs | the proof process that lasted for three hundred years | what did it leave to human beings?

 就是数学家沉浸在自己的 | 纯粹数学的思考里 | 他们在做那些研究的时候 | 根本没有想过 | 这些东西有什么用 | 不管是当时过是后来有什么用 | 他完全没有想过 | 但是这样关起门来 | 做的纯粹数学研究 | 后来被发现非常有用 | 所有人都感到困惑 | 但是不能解释这是为什么。Jiùshì shùxué jiā chénjìn zài zìjǐ de | chúncuì shùxué de sīkǎo lǐ | tāmen zài zuò nàxiē yánjiū de shíhòu | gēnběn méiyǒu xiǎngguò | zhèxiē dōngxī yǒu shé me yòng | bùguǎn shì dāngshíguò shì hòulái yǒu shé me yòng | tā wánquán méiyǒu xiǎngguò | dànshì zhèyàng guān qǐ mén lái | zuò de chúncuì shùxué yánjiū | hòulái pī fà xiàn fēicháng yǒuyòng | suǒyǒu rén dōu gǎndào kùnhuò | dànshì bùnéng jiěshì zhè shì wèishéme. – It is the mathematician who is immersed in his own | pure mathematical thinking | when they were doing those studies | never thought about | what use these things are | So behind closed doors | pure mathematical research done | turned out to be very useful later | everyone was confused | but couldn’t explain why.

一个-一开放等于多少那就有虚数 | 可能最早的时候 | 还不知道用 | 但是如果现在我们这个社会 | 如果没有虚数 | 你就没法刻画那个电磁场这些东西 | 你整个电学 | 你今天摄影师来照我需要电 | 没有电 | 这个社会可以想象吗?

Yīgè-yī kāifàng děngyú duōshǎo nà jiù yǒu xūshù | kěnéng zuìzǎo de shíhòu | hái bù zhīdào yòng | dànshì rúguǒ xiànzài wǒmen zhège shèhuì | rúguǒ méiyǒu xūshù | nǐ jiù méi fǎ kèhuà nàgè diàncíchǎng zhèxiē dōngxī | nǐ zhěnggè diànxué | nǐ jīntiān shèyǐng shī lái zhào wǒ xūyào diàn | méiyǒu diàn | zhège shèhuì kěyǐ xiǎngxiàng ma?

– One – how much is equal to one opening, then there are imaginary numbers | Maybe the earliest time | I don’t know how to use it | But if we are in this society now | If there are no imaginary numbers | I need electricity | No electricity | Is this society conceivable?

费马大定理 并不能真接改变我们的生活 | 人们最终也不知道 | 当年的费马到底有没有真正发现 | 那 美妙的证法 | 因为最后成功证明的种种数学工具 | 是三百年前还未出现的。Fèi mǎ dà dìnglǐ bìng bùnéng zhēn jiē gǎibiàn wǒmen de shēnghuó | rénmen zuìzhōng yě bù zhīdào | dāngnián de fèi mǎ dàodǐ yǒu méiyǒu zhēnzhèng fāxiàn | nà měimiào de zhèng fǎ | yīnwèi zuìhòu chénggōng zhèngmíng de zhǒngzhǒng shùxué gōngjù | shì sānbǎi nián qián hái wèi chūxiàn de. – „Fermat’s Last Theorem” can’t really change our lives | People don’t know in the end | Did Fermat really discover it | That „beautiful proof” | Because the mathematical tools that were finally successfully proved | are three It didn’t exist a hundred years ago.

而无数证明 费马大定理 不断失败的数学家 | 在探索这个迷宫的黑暗道路上 | 不断创造新的数学思想 | 不断开辟新的数学分支 | 那些因 费马大定理 而诞生的 | 划时代的研究 | 深远影响了现代数学 | 而这些数学知识 | 成为其它学科 | 改变我们真实世界的核心推动力。Ér wúshù zhèngmíng fèi mǎ dà dìnglǐ bùduàn shībài de shùxué jiā | zài tànsuǒ zhège mígōng de hēi’àn dàolù shàng | bùduàn chuàngzào xīn de shùxué sīxiǎng | bùduàn kāipì xīn de shùxué fēnzhī | nàxiē yīn fèi mǎ dà dìnglǐ ér dànshēng de | huàshídài de yánjiū | shēnyuǎn yǐngxiǎngle xiàndài shùxué | ér zhèxiē shùxué zhīshì | chéngwéi qítā xuékē | gǎibiàn wǒmen zhēnshí shìjiè de héxīn tuīdòng lì. – And countless mathematicians who prove „Fermat’s Last Theorem” keep failing | On the dark road of exploring this labyrinth | Constantly creating new mathematical ideas | Constantly opening up new branches of mathematics | Those born because of „Fermat’s Last Theorem” | Epoch-making research | has profoundly influenced modern mathematics | and these mathematical knowledge | become the core driving force for other disciplines | to change our real world.

而这一切源于一行写在数学书页上的不辨真假的灵光一现。Ér zhè yīqiè yuán yú yīxíng xiě zài shùxué shūyè shàng de bù biàn zhēn jiǎ de língguāng yī xiàn. – And it all stems from an indistinguishable flash of light written on the page of a math book.

可以说数学智慧是人类最高境界最高级别的智慧 | 但是数学家 | 他是一个认死理 | 不笨功夫的那个一类人 | 他们不惜花费一生的精力 | 来研究绝大多数人看起来 | 无用的学问 | 而且他今天创立的学问 | 也许将来会有用 | 但是这个奖来也许是十年以后 | 也许是一万年以后 | 他自己都看不见 | 但是他愿意在这样的事情上 | 不笨功夫 | 为人类和累可以说 | 最基本的智力的成果。

Kěyǐ shuō shùxué zhìhuì shì rénlèi zuìgāo jìngjiè zuìgāo jíbié de zhìhuì | dànshì shùxué jiā | tā shì yīgè rènsǐlǐ | bù bèn gōngfū dì nàgè yī lèi rén | tāmen bùxī huāfèi yīshēng de jīnglì | lái yánjiū jué dà duōshù rén kàn qǐlái | wúyòng de xuéwèn | érqiě tā jīntiān chuànglì de xuéwèn | yěxǔ jiānglái huì yǒuyòng | dànshì zhège jiǎng lái yěxǔ shì shí nián yǐhòu | yěxǔ shì yī wàn nián yǐhòu | tā zìjǐ dōu kàn bùjiàn | dànshì tā yuànyì zài zhèyàng de shìqíng shàng | bù bèn gōngfū | wéi rénlèi hé lèi kěyǐ shuō | zuì jīběn de zhìlì de chéngguǒ.

– It can be said that mathematical wisdom is the highest level of human intelligence | But mathematicians | He is a kind of person who admits to death | is not stupid | | And the knowledge he created today | may be useful in the future | but this prize may come ten years later | may be ten thousand years later | he can’t see it himself | but he is willing to do such things | Human beings and tired can be said | the most basic intellectual achievement.

的就是 | 数学的无用就是有用 | 为什么 | 如果我们把数学看成一个 | 创造性地工作的话 | 有用的那都创造出来的 | 无用的才是待开发待创造的 | 所以大家千万不要觉得 | 你这个数学搞什么 | 你的那些公式 | 你的那些定理能够派上用场吗 | 我在这里可以斩钉截铁地说 | 绝对能 | 因为迄今为止 | 这没有哪个数学 | 被发明出来以后 | 不能在实际当中派上用场。

Yào cóng gōngpíng de jiǎodù qù kǎolǜ | wǒ xiǎng yīgè shì yào rèn qīng de jiùshì | shùxué de wúyòng jiùshì yǒuyòng | wèishéme | rúguǒ wǒmen bǎ shùxué kàn chéng yīgè | chuàngzàoxìng dì gōngzuò dehuà | yǒuyòng dì nà dōu chuàngzào chūlái de | wúyòng de cái shì dài kāifā dài chuàngzào de | suǒyǐ dàjiā qiān wàn bùyào juédé | nǐ zhège shùxué gǎo shénme | nǐ dì nàxiē gōngshì | nǐ dì nàxiē dìnglǐ nénggòu pài shàng yòngchǎng ma | wǒ zài zhèlǐ kěyǐ zhǎndīngjiétiě de shuō | juéduì néng | yīnwèi qìjīn wéizhǐ | zhè méiyǒu nǎge shùxué | pī fà míng chūlái yǐhòu | bùnéng zài shíjì dāngzhōng pài shàng yòngchǎng.

– Consider it from a fair perspective | I think one thing to recognize is | the uselessness of mathematics is useful | why | if we think of mathematics as a | creative work | useful things are created | It is to be developed and created| So don’t think| There is no mathematics | after it has been invented | that cannot be used in practice.

数学大多数时候看起来 | 都没有什么用 | 特别是那种快速的即时的功用 | 一个新的数学成果被创造出来 | 很难在短时间内被转化为财富 | 对这个日新月异 | 急速前进的时代 | 和某些人来说 | 恐怕是难以接受的 | 谁也不知道 | 哪一个数学理论 | 会在什么时候成为主用 | 哥德巴赫猜想 | 至今也没有被派上用场 | 他所关心的整数的各种性质 | 数学家们已经为此 | 研究了二千多年 | 直到上世纪七十年代 | 其中的某些理论 | 才第一次被转化为具体的应用 | 人们依靠数论 | 建立起了现代密码学 | 我们今天的每一笔网络支付 | 都离下开它 | 不知道你对  哥德巴赫猜想 | 到底有什么用 | 是否有自己的答案。。。

Shùxué dà duōshù shíhòu kàn qǐlái | dōu méiyǒu shé me yòng | tèbié shì nà zhǒng kuàisù de jíshí de gōngyòng | yīgè xīn de shùxué chéngguǒ bèi chuàngzào chūlái | hěn nán zài duǎn shíjiān nèi bèi zhuǎnhuà wéi cáifù | duì zhège rìxīnyuèyì | jísù qiánjìn de shídài | hé mǒu xiē rén lái shuō | kǒngpà shì nányǐ jiēshòu de | shéi yě bù zhīdào | nǎ yīgè shùxué lǐlùn | huì zài shénme shíhòu chéngwéi zhǔ yòng | gē dé bāhè cāixiǎng | zhìjīn yě méiyǒu bèi pài shàng yòngchǎng | tāsuǒ guānxīn de zhěng shǔ de gè zhǒng xìngzhì | shùxué jiāmen yǐjīng wèi cǐ | yánjiūle èrqiān duō nián | zhídào shàng shìjì qīshí niándài | qízhōng de mǒu xiē lǐlùn | cái dì yī cì bèi zhuǎnhuà wéi jùtǐ de yìngyòng | rénmen yīkào shùlùn | jiànlì qǐle xiàndài mìmǎ xué | wǒmen jīntiān de měi yī bǐ wǎngluò zhīfù | dōu lí xià kāi tā | bù zhīdào nǐ duì gē dé bāhè cāixiǎng | dàodǐ yǒu shé me yòng | shìfǒu yǒu zìjǐ de dáàn…

– Mathematics looks most of the time | useless | especially the kind of fast instant utility | a new mathematical result is created | it is difficult to be converted into wealth in a short time | for this era of rapid change | | For some people | I am afraid it is unacceptable | no one knows | which mathematical theory | will be the main use | „Goldbach conjecture” | Various properties of integers | Mathematicians have done this | researched for more than 2,000 years | It was not until the 1970s | some of these theories | were translated into specific applications for the first time | people rely on number theory | modern cryptography | every online payment we make today | leave it | don’t know what your „Goldbach conjecture” | is useful | whether you have your own answer. . .

 

https://www.youtube.com/embed/EI28cPfZnTo?start=00

 

 

 

《被数学选中的人》第1 Chosen By Mathematics EP1 提起数学 你会想到什么?加减乘除 几何高数 还是上学时被支配的恐惧?【CCTV纪录】“Bèi shùxué xuǎnzhōng de rén” dì 1 jí Chosen By Mathematics EP1 tíqǐ shùxué nǐ huì xiǎngdào shénme? Jiā jiǎn chéngchú jǐhé gāo shù háishì shàngxué shí “bèi zhīpèi de kǒngjù”?[CCTV jìlù]– The Chosen By Mathematics Episode 1 Chosen By Mathematics EP1 When you think of mathematics, what comes to your mind? Addition, subtraction, multiplication and division, geometric high numbers, or the „fear of being dominated” in school? 【CCTV record】

本期内容:数学是我们生命中最抽象又最实用的一门学科,几乎所有学科都是在数学的指导下实现和演进的。总有一些人,他们对数学有着天生的敏感,始终被数学眷顾,正是因为他们的存在,如此艰深抽象的数学,才能孤傲的站立在科学的潮头,我们把他们称为被数学选中的人Běn qí nèiróng: Shùxué shì wǒmen shēngmìng zhòng zuì chōuxiàng yòu zuì shíyòng de yī mén xuékē, jīhū suǒyǒu xuékē dōu shì zài shùxué de zhǐdǎo xià shíxiàn hé yǎnjìn de. Zǒng yǒu yīxiē rén, tāmen duì shùxué yǒuzhe tiānshēng de mǐngǎn, shǐzhōng bèi shùxué juàngù, zhèng shì yīnwèi tāmen de cúnzài, rúcǐ jiānshēn chōuxiàng de shùxué, cáinéng gū’ào de zhànlì zài kēxué de cháo tóu, wǒmen bǎ tāmen chēng wèi “bèi shùxué xuǎnzhōng de rén”. – Contents of this issue: Mathematics is the most abstract and practical subject in our life. Almost all subjects are realized and evolved under the guidance of mathematics. There are always some people who have a natural sensitivity to mathematics and are always favored by mathematics. It is precisely because of their existence that such difficult and abstract mathematics can stand proudly at the forefront of science. We call them „selected by mathematics”. people”.

 

第一集

数学是什么

被数学选中的人

Dì yī jí shùxué shì shénme bèi shùxué xuǎnzhōng de rén

– Episode 1

what is math

chosen by mathematics

数学大概是我们生命中 Shùxué dàgài shì wǒmen shēngmìng zhòng  – Mathematics is probably our life

最抽象又最实用的一门学科。Zuì chōuxiàng yòu zuì shíyòng de yī mén xuékē. – The most abstract and practical subject.

它带给不同人的感受也大相径庭。Tā dài gěi bùtóng rén de gǎnshòu yě dàxiāngjìngtíng. – It brings different feelings to different people.

有的人甘之若饴。Yǒu de rén gān zhī ruò yí.– Some people are happy.

有的人恨之入骨。Yǒu de rén hèn zhī rùgǔ. – Some people hate it.

不管是喜欢还是讨厌。Bùguǎn shì xǐhuān háishì tǎoyàn. – Whether you like it or hate it.

数学抽象,数学运算,直观想象,逻辑推理 Shùxué chōuxiàng, shùxué yùnsuàn, zhíguān xiǎngxiàng, luójí tuīlǐ – Mathematical abstraction, mathematical operation, intuitive imagination, logical reasoning

当我们轻松地完成一次扫码支付时。Dāng wǒmen qīngsōng de wánchéng yīcì sǎo mǎ zhīfù shí. – When we easily complete one scan code payment.

数学的艰深与实用 Shùxué de jiānshēn yǔ shíyòng – Difficulty and practicality of mathematics

在此刻达了完美统一 Zài cǐkè dále wánměi tǒngyī – perfect unity at this moment

从小学生都会的加减乘除。Cóng xiǎoxuéshēng dūhuì de jiā jiǎn chéngchú.  – From elementary school students can add, subtract, multiply and divide.

 

到复杂到全世界只有几个人能看懂的推理演算从我们住的房子用的手机听得音乐到物理化学天文气象经济等等几乎所有学科都是在数学的指导下实现和演进的。Dào fùzá dào quán shìjiè zhǐyǒu jǐ gèrén néng kàn dǒng de tuīlǐ yǎnsuàn cóng wǒmen zhù de fángzi yòng de shǒujī tīng dé yīnyuè dào wùlǐ huàxué tiānwén qi xiàng jīngjì děng děng jīhū suǒyǒu xuékē dōu shì zài shùxué de zhǐdǎo xià shíxiàn hé yǎnjìn de. – From the reasoning and calculus so complicated that only a few people in the world can understand it, from listening to music on the mobile phone in the house we live in, to physics, chemistry, astronomy, meteorology, economics, and so on, almost all disciplines are realized and evolved under the guidance of mathematics.

总有一些人他们对数学有着天生的敏感始终被数学眷顾正是因为他们的存在如此艰深抽象的数学才能孤傲的站立在科学的潮头。Zǒng yǒu yīxiē rén tāmen duì shùxué yǒuzhe tiānshēng de mǐngǎn shǐzhōng bèi shùxué juàngù zhèng shì yīnwèi tāmen de cúnzài rúcǐ jiānshēn chōuxiàng de shùxué cáinéng gū’ào de zhànlì zài kēxué de cháo tóu. – There are always some people who have a natural sensitivity to mathematics and are always favored by mathematics. It is precisely because of their existence that such difficult and abstract mathematics can stand proudly at the forefront of science.

我们把他们称为被数学选中的人Wǒmen bǎ tāmen chēng wèi bèi shùxué xuǎnzhōng de rén – We call them „the ones chosen by mathematics”

神奇的是 Shénqí de shì  – miracly

虽然我们生命中遇到的一切事物都和数学有关我们却看不见摸不到它。Suīrán wǒmen shēngmìng zhòng yù dào de yīqiè shìwù dōu hé shùxué yǒuguān wǒmen què kàn bùjiàn mō bù dào tā. – Although everything we encounter in our life is related to mathematics, we cannot see or touch it.

数学的整个架构是人类在寻求万物规律时人为定义出来的也就是说数学是我们想出来的它只存在于我们的大脑里却真实地符合万物的规律这实在是一件奇妙的事那么我们片。Shùxué de zhěnggè jiàgòu shì rénlèi zài xúnqiú wànwù guīlǜ shí rénwéi dìngyì chūlái de yě jiùshì shuō shùxué shì wǒmen xiǎng chūlái de tā zhǐ cúnzài yú wǒmen de dànǎo lǐ què zhēnshí dì fúhé wànwù de guīlǜ zhè shízài shì yī jiàn qímiào de shì nàme wǒmen piàn. – The entire structure of mathematics is artificially defined by human beings when they seek the laws of all things. That is to say, mathematics is what we came up with. It only exists in our brains, but it truly conforms to the laws of all things. This is really a wonderful thing.

中这些 被数学选中的人 他们会用什么词来形容数学呢控制力性感天马行空?Zhōng zhèxiē bèi shùxué xuǎnzhōng de rén tāmen huì yòng shénme cí lái xíngróng shùxué ne kòngzhì lì xìnggǎn tiānmǎxíngkōng? – In these „people chosen by mathematics”, what words would they use to describe mathematics, control, sexy and unrestrained?

韩艾

互联网公司

算法工程师

Hán ài hùliánwǎng gōngsī suànfǎ gōngchéngshī

– Han Ai

Internet company

algorithm engineer

纯粹 Chúncuì  – purely

简单,深刻,普遍,对称 Jiǎndān, shēnkè, pǔbiàn, duìchèn – simple, profound, universal, symmetrical

潘宣余 Pānxuānyú – Pan Xuanyu

中科院数学与系统科学研究院副研究员 Zhōngkēyuàn shùxué yǔ xìtǒng kēxué yán jiù yuàn fù yánjiùyuán – Associate Researcher, Institute of Mathematics and Systems Science, Chinese Academy of Sciences

逻辑性很强,公式很美 Luójí xìng hěn qiáng, gōngshì hěn měi – The logic is very strong, the formula is beautiful

你看了就就喜欢说不上来。Nǐ kànle jiù jiù xǐhuān shuōbushàng lái. – When you see it, you like it and you can’t say it.

而且可能会有用。Érqiě kěnéng huì yǒuyòng. – And it might be useful.

邵昊华东师范大学学生 Shào hào huádōng shīfàn dàxué xuéshēng – Shao Hao – East China Normal University student

很有层次感的一门学科 Hěn yǒu céngcì gǎn de yī mén xué – A very hierarchical discipline

它比较干净 Tā bǐjiào gānjìng – it’s cleaner

徐佳轶 Xú jiā yì – Xu Jiayi

比较浪漫的 Bǐjiào làngmàn de – more romantic

刺激的 Cìjī de – stimulating

李艳:数学是很合理的。Lǐ yàn: Shùxué shì hěn hélǐ de. – Li Yan: Mathematics is very reasonable.

杜嘉铭:它是基本是无懈可击的就因为这个。Dùjiāmíng: Tā shì jīběn shì wúxièkějī de jiù yīnwèi zhège. – Du Jiaming: It is basically impeccable because of this.

它也比较给人安全感其实说。Tā yě bǐjiào jǐ rén ānquán gǎn qíshí shuō. – It also gives a more sense of security actually.

谢松宴:数学是这个样了的苏轼说过:横看成岭侧成峰远近高低各不同Xièsōngyàn: Shùxué shì zhège yàngle de sūshì shuōguò:Héng kàn chéng lǐng cè chéng fēng yuǎnjìn gāodī gè bùtóng. – Xie Songyan: Mathematics is like this, Su Shi said: „Look at the side of the ridge, the peaks are different in distance and height.”

每个人看到数学的面相不太一样。我看到的数学的面相它确实非常和谐非常引人入胜。Měi gèrén kàn dào shùxué de miànxiàng bù tài yīyàng. Wǒ kàn dào de shùxué de miànxiàng tā quèshí fēicháng héxié fēicháng yǐnrénrùshèng. – Everyone sees mathematics differently. The face of mathematics I see is really harmonious and fascinating.

如果你手上有一只苹果或者有一只篮球我不管你手上拿的是什么我用一样的力丢出去。Rúguǒ nǐ shǒu shàng yǒuyī zhǐ píngguǒ huòzhě yǒuyī zhǐ lánqiú wǒ bùguǎn nǐ shǒu shàng ná de shì shénme wǒ yòng yīyàng de lì diū chūqù. – If you have an apple in your hand or a basketball I don’t care what you have in your hand I will throw it with the same force.

我能描述它的不降的轨迹这个轨迹只要一个方程就可以描述将千千万万的现象用一个方程能描述然后这种就是简单。Wǒ néng miáoshù tā de bù jiàng de guǐjī zhège guǐjī zhǐyào yīgè fāngchéng jiù kěyǐ miáoshù jiāng qiān qiān wàn wàn de xiànxiàng yòng yīgè fāngchéng néng miáoshù ránhòu zhè zhǒng jiùshì jiǎndān. – I can describe its non-falling trajectory. This trajectory can be described by only one equation. Thousands of phenomena can be described by one equation, and this is simple.

就是因为它具备了又(有)控制了看似严谨的理性然后又具备天马行空这样一种非常感性然后又大胆的状态很野所以它自然就很性感。Jiùshì yīnwèi tā jùbèile yòu (yǒu) kòngzhìle kàn shì yánjǐn de lǐxìng ránhòu yòu jùbèi tiānmǎxíngkōng zhèyàng yī zhǒng fēicháng gǎnxìng ránhòu yòu dàdǎn de zhuàngtài hěn yě suǒyǐ tā zìrán jiù hěn xìnggǎn. – It is because it has and (has) controlled the seemingly rigorous rationality and then has a very emotional and then bold state, which is very wild, so it is naturally very sexy.

在数学家眼中数学充满着如恋人般的魅力但对大部分普通人来说数学代表着深奥枯燥绞尽脑汁并屡屡束手无策为什么我们和这些被数学选中的人感受如此大相径庭呢?Zài shùxué jiā yǎnzhōng shùxué chōngmǎnzhe rú liànrén bān de mèilì dàn duì dà bùfèn pǔtōng rén lái shuō shùxué dàibiǎozhuó shēn’ào kūzào jiǎo jǐn nǎozhī bìng lǚlǚ shùshǒuwúcè wèishéme wǒmen hé zhèxiē bèi shùxué xuǎnzhōng de rén gǎnshòu rúcǐ dàxiāngjìngtíng ne? – In the eyes of mathematicians, mathematics is full of love-like charm, but to most ordinary people, mathematics represents esoteric, boring, brain-draining, and often helpless. Why do we feel so different from these „people who are chosen by mathematics”?

我们有心要了解一下数学是如何在人类世界诞生和展的当我们明白了令人头疼的定理公式证是如何一步步出现并与人类互动的我们会意识到课堂上学到的可能真的不完全叫数学。Wǒmen yǒuxīn yào liǎo jiè yīxià shùxué shì rúhé zài rénlèi shìjiè dànshēng hé zhǎn dí dàng wǒmen míngbáile lìng rén tóuténg de dìnglǐ gōngshì zhèng shì rúhé yībù bù chūxiàn bìng yǔ rénlèi hùdòng de wǒmen huì yìshí dào kètáng shàngxué dào de kěnéng zhēn de bù wánquán jiào shùxué. – We want to understand how mathematics was born and developed in the human world. When we understand how the headaches of formula proofs emerge and interact with humans step by step, we realize that what we learn in class may not really be called completely. math.

没有人知道数学是什么时候是如何在人类族群中诞生的最早的考古物证是在非洲南部出士的一块狒狒的腓骨上面清晰地呈现二十九道 V 字形刻痕它距今约三万七千年它的用途有可能是记录的间的变迁。Méiyǒu rén zhīdào shùxué shì shénme shíhòu shì rúhé zài rénlèi zúqún zhōng dànshēng de zuìzǎo de kǎogǔ wùzhèng shì zài fēizhōu nánbù chū shì dì yīkuài fèifèi de féigǔ shàngmiàn qīngxī de chéngxiàn èrshíjiǔ dào V zìxíng kè hén tā jù jīn yuē sān wàn qīqiān nián tā de yòngtú yǒu kěnéng shì jìlù de jiān de biànqiān. – No one knows when and how mathematics was born. The earliest archaeological evidence is a fibula of a baboon from southern Africa. There are clearly twenty-nine „V”-shaped incisions on it. It is about 30,000 years old. Its use over the seven thousand years may have been a change between records.

一九六零年 Yījiǔliù líng nián  – 1960

比利时考古学家在非洲南部伊尚戈地区发掘出了一根狒狒腓骨。Bǐlìshí kǎogǔ xué jiā zài fēizhōu nánbù yī shàng gē dìqū fājué chūle yī gēn fèifèi féigǔ. – Belgian archaeologists have unearthed a baboon fibula in the Ishango region of southern Africa.

它制作于约两万年前。骨头上的刻痕分成不对称的三列这引起了科学家的无限遐想例如被用来作为一个计算工具用于简单的数学流程或者用来构造一个数字系统。当然也有人认为这些图案被过度解读了。Tā zhìzuò yú yuē liǎng wàn nián qián. Gǔtou shàng de kè hén fēnchéng bù duìchèn de sān liè zhè yǐnqǐle kēxuéjiā de wúxiàn xiáxiǎng lìrú bèi yòng lái zuòwéi yīgè jìsuàn gōngjù yòng yú jiǎndān de shùxué liúchéng huòzhě yòng lái gòuzào yīgè shùzì xìtǒng. Dāngrán yěyǒu rén rènwéi zhèxiē túàn bèi guòdù jiědúle. – It was made about 20,000 years ago. The nicks on the bones are divided into three asymmetrical columns which have sparked the imagination of scientists, for example as a computational tool for simple mathematical processes or for the construction of a number system. Of course, some people think that these patterns are over-interpreted.

这些刻痕可能只是为了增加抓握时的摩擦力这块 伊尚戈骨 长久以来成为窥远古人类对数学理解的重要证物。Zhèxiē kè hén kěnéng zhǐshì wèile zēngjiā zhuā wò shí de mócā lì zhè kuài yī shàng gē gǔ chángjiǔ yǐlái chéngwéi kuī yuǎngǔ rénlèi duì shùxué lǐjiě de zhòngyào zhèng wù. – These nicks may just be to increase the friction when grasping. This „Ishango bone” has long been an important evidence of ancient human understanding of mathematics.

人类大概是从七万年前开始走出撒哈拉大沙漠的就是靠着这个协同协作然后代代繁衍不断地奋斗慢慢地扩张到了这个地球的每一个角落有了我们现在这个世界的局面细想是一个很夏杂的动力系统里面必然后很深刻的数学公元前三千年四千年那个样子他忽然间地意识到五只羊和五头牛有一个共性就是这个五他把这个五抽象出来了。Rénlèi dàgài shì cóng qī wàn nián qián kāishǐ zǒuchū sǎhālā dà shāmò de jiùshì kàozhe zhège xiétóng xiézuò ránhòu dài dài fányǎn bùduàn de fèndòu màn man de kuòzhāng dàole zhège dìqiú de měi yīgè jiǎoluò yǒule wǒmen xiànzài zhège shìjiè de júmiàn xì xiǎng shì yīgè hěn xià zá de dònglì xìtǒng lǐmiàn bìrán hòu hěn shēnkè de shùxué gōngyuán qián sānqiānnián sìqiān nián nàgè yàngzi tā hūrán jiān dì yìshí dào wǔ zhǐ yáng hé wǔ tóu niú yǒu yīgè gòngxìng jiùshì zhège wǔ tā bǎ zhège wǔ chōuxiàng chūláile. – Human beings began to walk out of the Sahara Desert about 70,000 years ago. It is through this collaboration, and the continuous struggle from generation to generation, it has slowly expanded to every corner of the earth. With our current situation in this world, if you think about it, it is a There must be very profound mathematics in the very complicated dynamic system. He suddenly realized that the five sheep and the five cows have one thing in common, which is the five. He abstracted the five.

他把这个五抽象出来了。这个就是人类认识上一个巨大的进步。他已经有数字抽象的概念了。Tā bǎ zhège wǔ chōuxiàng chūláile. Zhège jiùshì rénlèi rènshí shàng yīgè jùdà de jìnbù. Tā yǐjīng yǒu shùzì chōuxiàng de gàiniànle. – He abstracted the five. This is a huge progress in human cognition. He already has the concept of digital abstraction.

我们至今也清楚 | 三万多年五千多年前 | 这段慢长的岁月里 | 数学在人类中是如何不断演进的 | 又有哪些在远古时代 | 就被数学选中的智者 | 依靠一己之力 | 使数学产生了跨越式的进步 | 两河流域的美索不达米亚文明 | 为后人留不了数学发展的物证 | 那是一些黏土泥板 | 上面记载了各种料密的运算表 | 比如倒数表平方表立方表 | 甚至更高次幂表  | 这个时期的数学称为巴比伦数学 | 黏上随处可寻 | 在潮湿的时候可以书写和修改 | 又可以长时间保存 | 这些古巴比伦人的习惯 | 使今天的我们得以了解 | 五千年前人类的数学水平 | 有些令现代人汗颜的是 | 我们今天相当多人的数学水准 | 远不及数千年前的古人。

Wǒmen zhìjīn yě qīngchǔ | sān wàn duō nián wǔqiān duō nián qián | zhè duàn màn zhǎng de suìyuè lǐ | shùxué zài rénlèi zhōng shì rúhé bùduàn yǎnjìn de | yòu yǒu nǎxiē zài yuǎngǔ shídài | jiù bèi shùxué xuǎnzhōng de zhìzhě | yīkào yījǐ zhī lì | shǐ shùxué chǎnshēngle kuàyuè shì de jìnbù | liǎng hé liúyù dì měi suǒ bù dá mǐ yà wénmíng | wèi hòu rén liú bùliǎo shùxué fāzhǎn de wùzhèng | nà shì yīxiē niántǔ ní bǎn | shàngmiàn jìzǎile gè zhǒng liào mì de yùnsuàn biǎo | bǐrú dàoshǔ biǎo píngfāng biǎo lìfāng biǎo | shènzhì gèng gāo cì mì biǎo | zhège shíqí de shùxué chēng wèi bābǐlún shùxué | nián shàng suíchù kě xún | zài cháoshī de shíhòu kěyǐ shūxiě hé xiūgǎi | yòu kěyǐ cháng shíjiān bǎocún | zhèxiē gǔ bābǐlún rén de xíguàn | shǐ jīntiān de wǒmen déyǐ liǎojiě | wǔqiān nián qián rénlèi de shùxué shuǐpíng | yǒuxiē lìng xiàndài rén hànyán de shì | wǒmen jīntiān xiàng dāng duō rén de shùxué shuǐzhǔn | yuǎn bùjí shù qiān nián qián de gǔrén.

– We still know | 30,000 years ago and 5,000 years ago | in this slow period of time | how mathematics has evolved in human beings | and which ones in ancient times | were selected by mathematics | Force | Made a leap forward in mathematics | Mesopotamian civilization in the Mesopotamia | No physical evidence of the development of mathematics for future generations | Those are some clay tablets | | such as reciprocal tables, square tables, cubic tables | even higher power tables | mathematics of this period is called Babylonian mathematics | glue can be found everywhere | can be written and modified when wet | The habit of | makes us understand today | the level of mathematics of human beings 5,000 years ago | Some modern people are ashamed that | the level of mathematics of many of us today | is far less than that of the ancients thousands of years ago.

在人类文明的早期数学是人们为了解决日常实际问题而自发创造出来的工具如何分配物资如何记录收支如何建造房屋等等都需要数学的帮助。Zài rénlèi wénmíng de zǎoqí shùxué shì rénmen wèi liǎo jiějué rìcháng shíjì wèntí ér zìfā chuàngzào chūlái de gōngjù rúhé fēnpèi wùzī rúhé jìlù shōu zhī rúhé jiànzào fángwū děng děng dōu xūyào shùxué de bāngzhù. – In the early days of human civilization, mathematics was a tool created spontaneously by people in order to solve daily practical problems. How to distribute materials, record income and expenditure, build houses, etc. all need the help of mathematics.

埃及文明的书写记录载体是莎草纸 | 这种易碎的物质能保存下来 | 体身就是一个奇迹 | 成书于三千六百年的莎草纸卷 | 莱因德古本莫斯科古本 上 | 记录了八十多个数学问题和解答 | 很多问题是和分面包有关的 | 这大概是由于古埃及人没有货币 | 而用面包和啤酒 | 来做交易标准的原因 | 有一道题是| 如何让十个人平分九片面包 | 也就是每个人怎么拿到十分之九片面包 | 古埃及人明显已经熟练掌握了 | 分数的运用 | 在莎草纸上。

Āijí wénmíng de shūxiě jìlù zàitǐ shì suō cǎozhǐ | zhè zhǒng yì suì de wùzhí néng bǎocún xiàlái | tǐ shēn jiùshì yīgè qíjī | chéngshū yú sānqiān liùbǎi nián de suō cǎozhǐ juǎn | lái yīn dé gǔběn hé mòsīkē gǔběn shàng | jìlùle bāshí duō gè shùxué wèntí hé jiědá | hěnduō wèntí shì hé fēn miànbāo yǒuguān de | zhè dàgài shì yóuyú gǔ āijí rén méiyǒu huòbì | ér yòng miànbāo hé píjiǔ | lái zuò jiāoyì biāozhǔn dì yuányīn | yǒu yīdào tí shì | rúhé ràng shí gèrén píngfēn jiǔ piàn miànbāo | yě jiùshì měi gèrén zěnme ná dào shí fēn zhī jiǔ piàn miànbāo | gǔ āijí rén míngxiǎn yǐjīng shúliàn zhǎngwòle | fēn shǔ de yùnyòng | zài suō cǎozhǐ shàng.

– The written record carrier of Egyptian civilization is papyrus | This fragile substance can be preserved | The body is a miracle | Written on 3600-year-old papyrus scrolls | On the „Rhind Book” and „Moscow Book” | More than 80 math problems and solutions are recorded | Many problems are related to dividing bread | This is probably because the ancient Egyptians did not have currency | and used bread and beer | as a trading standard | One question is | How Let ten people divide nine slices of bread equally | That is, how does each get nine tenths of bread | The ancient Egyptians apparently mastered it | the use of fractions | on papyrus.

这道题的答案是十分之九等于三分之二加五分之一加三十分之一。Zhè dào tí de dáàn shì shí fēn zhī jiǔ děngyú sān fēn zhī èr jiā wǔ fēn zhī yī jiā sānshí fēn zhī yī. – The answer to this question is nine-tenths equals two-thirds plus one-fifth plus one-thirtieth.

 实际的操作方法是 | 将其中五片平均分二块 | 正好十块每人拿一块 | 把乘余四平均分成三块 | 一共十二小块每人再拿一块 | 还乘二小块 | 把这二小块每块每平均分成五块 | 这样每个人又可以再拿一块 | 正好平均分完 | 这样切的话 | 每个人分得的面包不但数量相等 | 连大小和块数也一样的。

Shíjì de cāozuò fāngfǎ shì | jiāng qízhōng wǔ piàn píngjūn fēn èr kuài | zhènghǎo shí kuài měi rén ná yīkuài | bǎ chéng yú sì píngjūn fēnchéng sān kuài | yīgòng shíèr xiǎo kuài měi rén zài ná yīkuài | hái chéng èr xiǎo kuài | bǎ zhè èr xiǎo kuài měi kuài měi píngjūn fēnchéng wǔ kuài | zhèyàng měi gèrén yòu kěyǐ zài ná yīkuài | zhènghǎo píngjūn fēn wán | zhèyàng qiè dehuà | měi gèrén fēn dé de miànbāo bùdàn shùliàng xiāngděng | lián dàxiǎo hé kuài shù yě yīyàng de.

– The actual operation method is | Divide the five pieces into two pieces evenly | Take exactly ten pieces and take one piece for each person | Divide the remainder of the multiplication into three pieces on average | Take a total of twelve small pieces and take another piece for each person | Multiply two small pieces | The two small pieces are divided into five pieces each equally | so that each person can take another piece | just as evenly divided | if cut in this way | each person will receive not only the same amount of bread | but also the same size and number of pieces.

 

在中国的记载中公元前一千年左右商高与周公对答的说 勾广三股修四径隅五 | 这里的勾就是小腿股是大腿 | 这是古人从自身身体上 | 发现并直角边 | 如果一边的长度是三另一边是四那么斜边的长度就是五。

Zài zhōngguó de jìzǎi zhōng gōngyuán qián yīqiān nián zuǒyòu shāng gāo yǔ zhōugōng duìdá de shuō gōu guǎng sāngǔ xiū sì jìng yú | zhèlǐ de gōu jiùshì xiǎotuǐ gǔ shì dàtuǐ | zhè shì gǔrén cóng zìshēn shēntǐ shàng | fāxiàn bìng zhíjiǎo biān | rúguǒ yībiān de chángdù shì sān lìng yībiān shì sì nàme xié biān de chángdù jiùshì wǔ.

– In Chinese records around the first millennium BC, Shang Gao and Zhou Gong replied, „Gouguang, three strands, four diameters and five corners” | The hook here is the calf and the thigh | This is from the ancients’ own body | | If the length of one side is three and the other side is four, then the length of the hypotenuse is five.

勾股定理几乎被所有远古文明独立发现大概是由于人们在丈量土地和建造房屋时要经常计算直角三角形的边长。

Gōu gǔ dìnglǐ jīhū bèi suǒyǒu yuǎngǔ wénmíng dúlì fāxiàn dàgài shì yóuyú rénmen zài zhàngliàng tǔdì hé jiànzào fángwū shí yào jīngcháng jìsuàn zhíjiǎo sānjiǎoxíng de biān zhǎng. – The Pythagorean Theorem was discovered independently by almost all ancient civilizations, probably because people often calculated the side lengths of right triangles when measuring land and building houses.

相传古埃及人用十二段等长的绳子围城一个坏形然后把其中五段拉直固定两端把另一边的绳子拉到一点拉紧就构成了一个直角三角形可以想见。Xiāngchuán gǔ āijí rén yòng shíèr duàn děng zhǎng de shéngzi wéichéng yīgè huài xíng ránhòu bǎ qízhōng wǔ duàn lā zhí gùdìng liǎng duān bǎ lìng yībiān de shéngzi lā dào yīdiǎn lā jǐn jiù gòuchéngle yīgè zhíjiǎo sānjiǎoxíng kěyǐ xiǎngjiàn. – According to legend, the ancient Egyptians used twelve equal-length ropes to surround a bad shape, then straightened five of them, fixed the two ends, and pulled the rope on the other side to a point and tightened to form a right-angled triangle.

古人通过多次尝试便可找到这一规律。他们把这样的绳套摆在地其上用以建造建筑的直角这是勾股定理在生活中自发而神奇的运用。Gǔrén tōngguò duō cì chángshì biàn kě zhǎodào zhè yī guīlǜ. Tāmen bǎ zhèyàng de shéng tào bǎi zài dì qí shàng yòng yǐ jiànzào jiànzhú de zhíjiǎo zhè shì gōu gǔ dìnglǐ zài shēnghuó zhōng zì fà ér shénqí de yùnyòng. – The ancients found this pattern through many attempts. They put such noose on the ground to construct the right angle of the building. This is the spontaneous and magical application of the Pythagorean theorem in life.

在古文明中数学的大部分概念就是数字。Zài gǔ wénmíng zhōng shùxué de dà bùfèn gàiniàn jiùshì shùzì. Most of the concepts of mathematics in ancient civilizations were numbers.

公元前五百年开始希腊文明使数学产生了重大突破。Gōngyuán qián wǔbǎi nián kāishǐ xīlà wénmíng shǐ shùxué chǎnshēngle zhòngdà túpò. In the fifth century BC, the Greek civilization made a major breakthrough in mathematics.

泰勒斯毕达哥拉斯柏拉图亚里土多德阿基米德这些如雷贯耳的名字把数学作为一门科学学科建立起来。Tài lè sī bì dá gē lā sī bólātú yà lǐ tǔ duō dé ā jī mǐ dé zhèxiē rúléiguàn’ěr de míngzì bǎ shùxué zuòwéi yī mén kēxué xuékē jiànlì qǐlái. Thales, Pythagoras, Plato, Aristotle, Archimedes, and the like, established mathematics as a scientific discipline.

希腊数学最突出的成就之一在于对几何的发展。Xīlà shùxué zuì túchū de chéngjiù zhī yī zàiyú duì jǐhé de fǎ zhǎn. One of the most prominent achievements of Greek mathematics lies in the development of geometry.

数学家希帕克斯使用相似三角形定理估算地球半径为三千九百四十四点三 (约合六千三百四十八公里)而现代科技测量结果为三千九百六十一点三英里。Shùxué jiā xī pàkè sī shǐyòng xiāngsì sānjiǎoxíng dìnglǐ gūsuàn dìqiú bànjìng wèi sānqiān jiǔbǎi sìshísì diǎn sān (yuē hé liùqiān sānbǎi sìshíbā gōnglǐ) ér xiàndài kējì cèliáng jiéguǒ wèi sānqiān jiǔbǎi liùshíyī diǎn sān yīnglǐ.

Mathematician Hippax used the similar triangle theorem to estimate the radius of the earth to be 3944.3 (about 6348 kilometers) while modern technology measures it to be 3961.3 miles .

约合六千三百七十五公里仅仅相差十七英里(约合二十七公里)。Yuē hé liùqiān sānbǎi qīshíwǔ gōnglǐ jǐnjǐn xiāngchà shíqī yīnglǐ (yuē hé èrshíqī gōnglǐ). About 6,375 kilometers is only a difference of seventeen miles (about 27 kilometers).

他估算地球到月球距离为二十三万英里 (约合三十八万三千零二十四公里。Tā gūsuàn dìqiú dào yuèqiú jùlí wéi èrshísān wàn yīnglǐ (yuē hé sānshíbā wàn sānqiān líng èrshísì gōnglǐ. He estimated the distance from the Earth to the Moon to be 230,000 miles (about 383,024 kilometers).

现代测量数据为二十四万英里(约合三十八万六千两百四十三公里误差只有百分之零点八。Xiàndài cèliáng shùjù wéi èrshísì wàn yīnglǐ (yuē hé sānshíbā wàn liùqiān liǎng bǎi sìshísān gōnglǐ wùchā zhǐyǒu bǎi fēn zhī líng diǎn bā.Modern measurements are 240,000 miles (386,243 kilometers) with an error of only 0.8 percent.

欧几里得是古希腊最著名的数学家之一。

Ōu jǐ lǐ dé shì gǔ xīlà zuì zhùmíng de shùxué jiā zhī yī.

Euclid was one of the most famous mathematicians of ancient Greece.

 

他在公元前三百年左右完成了《几何原本》。Tā zài gōngyuán qián sānbǎi nián zuǒyòu wánchéngle “jǐhé yuánběn”. He completed the Elements around 300 BC.

它深远影响了后来整个欧洲的数学也是世界上最成功的教科书。Tā shēnyuǎn yǐngxiǎngle hòulái zhěnggè ōuzhōu de shùxué yěshì shìjiè shàng zuì chénggōng de jiàokēshū. It has a profound impact on mathematics throughout Europe and is the most successful textbook in the world.

《几何原本》把当时人类掌握的几何知识以一种极度严密的逻辑关系联结起来使数学。“Jǐhé yuánběn” bǎ dāngshí rénlèi zhǎngwò de jǐhé zhīshì yǐ yī zhǒng jídù yánmì de luójí guānxì liánjié qǐlái shǐ shùxué. „Elements of Geometry” combined the geometric knowledge mastered by humans at that time with an extremely strict logical relationship to make mathematics.

这门学科体系化直到今天全世界中小学生学习的大部分几何知识都囊括在这体两千多年前的教科书里。Zhè mén xuékē tǐxì huà zhídào jīntiān quán shìjiè zhōng xiǎoxuéshēng xuéxí de dà bùfèn jǐhé zhīshì dōu nángkuò zài zhè tǐ liǎng qiān duō nián qián de jiàokēshū lǐ.This discipline is systematized until today, and most of the geometry knowledge learned by primary and secondary school students all over the world is included in this textbook more than 2,000 years ago.

数学在全人类智者孜孜不倦地追求之下由一种从生产生活中总结出来的工具。Shùxué zài quán rénlèi zhìzhě zīzībùjuàn de zhuīqiú zhī xià yóu yī zhǒng cóng shēngchǎn shēnghuó zhōng zǒngjié chūlái de gōngjù. – Mathematics is a tool summed up from production and life under the tireless pursuit of all human beings.

历经代数学的发展解析几何的出现微积分的创立函数概念的发明非欧几何的研究应用数学的蓬勃逐渐演变为引领整个自然科学发展的知识体系为了生产生活人类发明了算术为了丈量土地计算面积人类又发明了几何为了量天测地又发明了三角近代以来人类面临的问题又更加地复杂比如说为了计算天体运动。

Lìjīng dài shùxué de fǎ zhǎn jiěxī jǐhé de chūxiàn wéi jīfēn de chuànglì hánshù gàiniàn de fǎ míng fēi ōu jǐhé de yánjiū yìngyòng shùxué de péngbó zhújiàn yǎnbiàn wèi yǐnlǐng zhěnggè zìrán kēxué fāzhǎn de zhīshì tǐxì wèile shēngchǎn shēnghuó rénlèi fāmíng liǎo suànshù wèile zhàngliàng tǔdì jìsuàn miànjī rénlèi yòu fāmíngliǎo jǐhé wèile liàng tiān cè de yòu fāmíngliǎo sānjiǎo jìndài yǐlái rénlèi miànlín de wèntí yòu gèngjiā de fùzá bǐrú shuō wèile jìsuàn tiāntǐ yùndòng.

– After the development of algebra, the emergence of analytic geometry, the creation of calculus, the invention of the concept of functions, the development of non-Euclidean geometry, the flourishing of applied mathematics, and gradually evolved into a knowledge system that leads the development of the entire natural sciences. Geometry was invented to measure the sky, and triangles were invented. The problems faced by human beings since modern times have become more complex, such as calculating the motion of celestial bodies.

人类又发明了微积分那么为了措述自然界的一些现象人类又发明出了常微分方程和偏微分方程等强有力的工具那么以至于到我们现代的最先进的数学。

Rénlèi yòu fāmíngliǎo wéi jīfēn nàme wèile cuò shù zìránjiè de yīxiē xiànxiàng rénlèi yòu fāmíng chūle cháng wéifēn fāngchéng hé piān wéifēn fāngchéng děng qiáng yǒulì de gōngjù nàme yǐ zhìyú dào wǒmen xiàndài de zuì xiānjìn de shùxué.

Humans have invented calculus, and in order to describe some phenomena in nature, humans have invented powerful tools such as ordinary differential equations and partial differential equations, and so on to our modern most advanced mathematics.

现在已经应用到5G技术 人工智能各个方面应该说人类文明的发展和数学是密切相关而且是正相关的

Xiànzài yǐjīng yìngyòng dào 5G jìshù réngōng zhìnéng gège fāngmiàn yīnggāi shuō rénlèi wénmíng de fǎ zhǎn hé shùxué shì mìqiè xiāngguān érqiě shìzhèng xiāngguān de.

Now that it has been applied to 5G technology, all aspects of artificial intelligence should be said that the development of human civilization and mathematics are closely and positively related.

我们数学就相当于做了一个知识库做了这么一个理论体系而其它的学科不管是物理或其它的计算机什么都可以把这个东西作为一个工具来用它我们只是造个工具。Wǒmen shùxué jiù xiāngdāng yú zuòle yīgè zhīshì kù zuòle zhème yīgè lǐlùn tǐxì ér qítā de xuékē bùguǎn shì wùlǐ huò qítā de jìsuànjī shénme dōu kěyǐ bǎ zhège dōngxī zuòwéi yīgè gōngjù lái yòng tā wǒmen zhǐshì zào gè gōngjù. – Our mathematics is equivalent to making a knowledge base to make such a theoretical system, and other disciplines, whether it is physics or other computers, can use this thing as a tool and use it, we just create a tool.

如果假设外面有个比我们更高级的生物弄个望远镜来看我们。

Rúguǒ jiǎshè wàimiàn yǒu gè bǐ wǒmen gèng gāojí de shēngwù nòng gè wàngyuǎnjìng lái kàn wǒmen.

Suppose there is a creature out there that is more advanced than us and looks at us with a telescope.

你如果看到我们比方说二万年以前的地球或者二千年以前的地球和现在大家想我吗这个星球。

Nǐ rúguǒ kàn dào wǒmen bǐfāng shuō èr wàn nián yǐqián dì dìqiú huòzhě èrqiān nián yǐqián dì dìqiú hé xiànzài dàjiā xiǎng wǒ ma zhège xīngqiú.

If you see us, for example, the earth 20,000 years ago or the earth 2,000 years ago and now, do people miss me this planet?

我们这个人类之所以这么进步这种神速真是不敢想象。

Wǒmen zhège rénlèi zhī suǒyǐ zhème jìnbù zhè zhǒng shénsù zhēnshi bù gǎn xiǎngxiàng.

It is unbelievable that we humans have made such rapid progress.

人类有了数学才会有后边所有的这些科学没有科学那个社会怎么进步?

所以从这一点怎么说数学的重要性都不为过。Rénlèi yǒule shùxué cái huì yǒu hòubian suǒyǒu de zhèxiē kēxué méiyǒu kēxué nàgè shèhuì zěnme jìnbù? Suǒyǐ cóng zhè yīdiǎn zěnme shuō shùxué de zhòngyào xìng dōu bù wéiguò. – With mathematics, human beings can have all these sciences that follow. Without science, how would a society progress? So it is hard to overstate the importance of mathematics from this point of view.

回到我们的主题数学是什么?们可以认为数学是打开各个自然学科大门的钥匙。Huí dào wǒmen de zhǔtí shùxué shì shénme? Men kěyǐ rènwéi shùxué shì dǎkāi gège zìrán xuékē dàmén de yàoshi.Back to our topic what is math? We can think of mathematics as the key that opens the doors of various natural disciplines.

数学自诞生起就一直推动着天文和物理学的发展。Shùxué zì dànshēng qǐ jiù yīzhí tuīdòngzhe tiānwén hé wùlǐ xué de fǎ zhǎn. ­Mathematics has been driving the development of astronomy and physics since its inception.

古希腊人采用大量的数学知识来解释和预测恒星与行星的位置。Gǔ xīlà rén cǎiyòng dàliàng de shùxué zhīshì lái jiěshì hé yùcè héngxīng yǔ xíngxīng de wèizhì. The ancient Greeks used a great deal of mathematics to explain and predict the positions of stars and planets.

伟大的天文学家托勒密建立了完整的星球运行横型。Wěidà de tiānwénxué jiā tuō lēi mì jiànlìle wánzhěng de xīngqiú yùnxíng héngxíng. The great astronomer Ptolemy established a complete planetary orbit.

当然现在我们知道它是错的。Dāngrán xiànzài wǒmen zhīdào tā shì cuò de. Of course now we know it was wrong.

地心说统治了人类二千多年直到十七世纪随着解析几何与微积分等一批重要数学成果的诞生牛顿的绝对时空理论横出世尽管它依然是错的。Dìxīnshuō tǒngzhìle rénlèi èrqiān duō nián zhídào shíqī shìjì suízhe jiěxī jǐhé yǔ wéi jīfēn děng yī pī zhòngyào shùxué chéngguǒ de dànshēng niúdùn de juéduì shíkōng lǐlùn héng chūshì jǐnguǎn tā yīrán shì cuò de. Geocentric theory ruled mankind for more than 2,000 years until the seventeenth century, with the birth of a number of important mathematical achievements such as analytic geometry and calculus, Newton’s absolute space-time theory was born, although it was still wrong.

但数学的方法论彻底改变了人类文明的进程影响了后来的整个科学体系。Dàn shùxué de fāngfǎlùn chèdǐ gǎibiànle rénlèi wénmíng de jìnchéng yǐngxiǎngle hòulái de zhěnggè kēxué tǐxì. But the methodology of mathematics completely changed the course of human civilization and affected the entire scientific system later.

一九一五年爱因斯坦发表了广义相对论人类对于时间和空间的认知终于走到了全新的阶段。Yījiǔyīwǔ nián ài yīn sītǎn fābiǎole guǎngyì xiāngduìlùn rénlèi duìyú shíjiān hé kōngjiān de rèn zhī zhōngyú zǒu dàole quánxīn de jiēduàn. In 1915, Einstein published his general theory of relativity. Humans’ cognition of time and space has finally reached a new stage.

而在此之前的一八五四年黎曼几何这样数学理论早已在那里等着爱因斯坦的出现。Ér zài cǐ zhīqián de yībāwǔsì nián lí màn jǐhé zhèyàng shùxué lǐlùn zǎoyǐ zài nàlǐ děngzhe ài yīn sītǎn de chūxiàn.Before that, in 1854, mathematical theories such as Riemannian geometry were already there waiting for the appearance of Einstein.

那么中国古代数学有一个词叫筹人。Nàme zhōngguó gǔdài shùxué yǒu yīgè cí jiào chóu rén.  – Well, in ancient Chinese mathematics, there is a word called „Chou Ren”.

所谓筹就是指从事天文和数学研究的人也就是说从古代来看数学和天文学是不分家的。Suǒwèi chóu jiùshì zhǐ cóngshì tiānwén hé shùxué yánjiū de rén yě jiùshì shuō cóng gǔdài lái kàn shùxué hé tiānwénxué shì bù fēn jiā de. – The so-called chip refers to those who are engaged in astronomy and mathematics research, which means that mathematics and astronomy are not separated from ancient times.

我们可以把数学理解成人的一条胳膊的人臂。Wǒmen kěyǐ bǎ shùxué lǐjiě chéngrén de yītiáo gēbó de rén bì.  – We can understand mathematics as the human arm of an adult’s one arm.

那么这条大壁它够不着宇宙模型那样的一个目标但是它在这个上面它有一个小臂那么这就是物理学。Nàme zhè tiáo dà bì tā gòu bùzháo yǔzhòu móxíng nàyàng de yīgè mùbiāo dànshì tā zài zhège shàngmiàn tā yǒu yīgè xiǎo bì nàme zhè jiùshì wùlǐ xué.  – Well, this big wall can’t reach a target like the universe model, but it has a small arm on top of it, so this is physics.

然后物理学再上边是天文学你就可以想象她文学就是长在这小臂上这只手那么这只手最后就抓到了那个宇宙模型。Ránhòu wùlǐ xué zài shàngbian shì tiānwénxué nǐ jiù kěyǐ xiǎngxiàng tā wénxué jiùshì zhǎng zài zhè xiǎo bì shàng zhè zhī shǒu nàme zhè zhī shǒu zuìhòu jiù zhuā dàole nàgè yǔzhòu móxíng. – Then on top of physics is astronomy, and you can imagine that her literature is the hand that grows on this forearm, then this hand finally grasps the model of the universe.

更具体来讲就是今天的宇宙学很大程度上是建立在爱因斯坦的广义相对论的基础之上的而广义相对论是直接地以带有张量形式的黎曼几何作为基础的。Gèng jùtǐ lái jiǎng jiùshì jīntiān de yǔzhòu xué hěn dà chéngdù shàng shì jiànlì zài ài yīn sītǎn de guǎngyì xiāngduìlùn de jīchǔ zhī shàng de ér guǎngyì xiāngduìlùn shì zhíjiē dì yǐ dài yǒu zhāng liàng xíngshì dí lí màn jǐhé zuòwéi jīchǔ de.  – More specifically, cosmology today is largely based on Einstein’s general theory of relativity, which is directly based on Riemannian geometry with tensor forms.

没有数学中的黎曼几何就没有爱因斯坦的广义相对论而没有广义相对论就不可能有宇宙学的今天的一个壮态。Méiyǒu shùxué zhōng dí lí màn jǐhé jiù méiyǒu ài yīn sītǎn de guǎngyì xiāngduìlùn ér méiyǒu guǎngyì xiāngduìlùn jiù bù kěnéng yǒu yǔzhòu xué de jīntiān de yīgè zhuàng tài. – Without Riemannian geometry in mathematics, there would be no Einstein’s general theory of relativity, and without general relativity, there would be no strong state of cosmology today.

但人们很难给数学下一个清晰完整的定义因为它是抽象的是连接人类抽象思维与现实世界的通道。Dàn rénmen hěn nán gěi shùxué xià yīgè qīngxī wánzhěng de dìngyì yīnwèi tā shì chōuxiàng de shì liánjiē rénlèi chōuxiàng sīwéi yǔ xiànshí shìjiè de tōngdào.  – But it is difficult for people to give a clear and complete definition of mathematics because it is abstract and is the channel connecting the abstract thinking of human beings with the real world.

它可以把抽象化的理论作用于现实指导人类不断改造世界更重要的。Tā kěyǐ bǎ chōuxiàng huà de lǐlùn zuòyòng yú xiànshí zhǐdǎo rénlèi bùduàn gǎizào shìjiè gèng zhòngyào de.  – It can put abstract theories into practice and guide human beings to continuously transform the world more importantly.

它把现实事物抽象化从而探究宇宙万物的规律。Tā bǎ xiànshí shìwù chōuxiàng huà cóng’ér tànjiù yǔzhòu wànwù de guīlǜ. – It abstracts real things to explore the laws of all things in the universe.

由此看来数学也是一种哲学。 Yóu cǐ kàn lái shùxué yěshì yī zhǒng zhéxué. – From this point of view, mathematics is also a kind of philosophy.

我想人类世界的结构是方方面面的。Wǒ xiǎng rénlèi shìjiè de jiégòu shì fāngfāngmiànmiàn de.  – I think the structure of the human world is multifaceted.

我们为什么人类喜欢结构?Wǒmen wèishéme rénlèi xǐhuān jiégòu?  – Why do we humans like structure?

因为结构带来了秩序。Yīnwèi jiégòu dài láile zhìxù.  – Because structure brings order.

我们其实最喜欢其实是秩序。Wǒmen qíshí zuì xǐhuān qíshí shì zhìxù. – What we actually like the most is actually order.

大自然的很多事物有时候就是和数学的这样的秩序是如此地吻合比如说冬天的雪花那么它们是很完美的六边形或者六边形的衍生物。

Dà zìrán de hěnduō shìwù yǒu shíhòu jiùshì hé shùxué de zhèyàng de zhìxù shì rúcǐ dì wěnhé bǐrú shuō dōngtiān de xuěhuā nàme tāmen shì hěn wánměi de liù biān xíng huòzhě liù biān xíng de yǎnshēng wù.  – Many things in nature are sometimes so consistent with this mathematical order, such as snowflakes in winter, so they are perfect hexagons or derivatives of hexagons.

它们都是由自相似的组成那么在数学上叫做分形。Tāmen dōu shì yóu zì xiāngsì de zǔchéng nàme zài shùxué shàng jiàozuò fēnxíng.  – They are both composed of self-similar components and are mathematically called fractals.

我们先不说这个概念。Wǒmen xiān bù shuō zhège gàiniàn.– Let’s leave this concept out of the way.

我们只说相似这个概念那么数学上有相似自然界也有相似。Wǒmen zhǐ shuō xiāngsì zhège gàiniàn nàme shùxué shàng yǒu xiāngsì zìránjiè yěyǒu xiāngsì.  – We only talk about the concept of similarity, so there is similarity in mathematics and there is similarity in nature.

这难道仅仅是巧合吗?Zhè nándào jǐnjǐn shì qiǎohé ma? – Is this just a coincidence?

大自然在进化过程中它很神奇。Dà zìrán zài jìnhuà guòchéng zhōng tā hěn shénqí. Nature is amazing in the process of evolution.

你就觉得它好像具备人类的思维一样。Nǐ jiù juédé tā hǎoxiàng jùbèi rénlèi de sīwéi yīyàng. You feel like it has the human mind.

比如说向日葵它种子结的时候表示出来这种螺线包括松果的螺线包括花瓣的生长。Bǐrú shuō xiàngrìkuí tā zhǒngzǐ jié de shíhòu biǎoshì chūlái zhè zhǒng luó xiàn bāokuò sōng guǒ de luó xiàn bāokuò huābàn de shēngzhǎng. For example, when the sunflower seeds are knotted, it shows that the spiral includes the spiral of the pine cone, including the growth of the petals.

它都表现出斐波那契数列这种特殊的模式。Tā dōu biǎoxiàn chū fěi bō nà qì shùliè zhè zhǒng tèshū de móshì.It all exhibits a special pattern of the Fibonacci sequence.

斐波那契数列是十三世纪的意大利数学家斐波那契通过 兔子问题引申出的一种数列排布。Fěi bō nà qì shùliè shì shísān shìjì de yìdàlì shùxué jiā fěi bō nà qì tōngguò tùzǐ wèntí” yǐnshēn chū de yī zhǒng shùliè pái bù. – The Fibonacci sequence is a sequence arrangement derived from the „rabbit problem” by the Italian mathematician Fibonacci in the thirteenth century.

有一对小兔它们两个月就可以变成可繁殖的大兔大兔月可以生一对小兔一年以后会有多少对兔子呢?Yǒuyī duì xiǎo tù tāmen liǎng gè yuè jiù kěyǐ biàn chéng kě fánzhí de dà tù dà tù yuè kěyǐ shēng yī duì xiǎo tù yī nián yǐhòu huì yǒu duōshǎo duì tùzǐ ne? – If you have a pair of little rabbits, they can become fertile big rabbits in two months. How many pairs of rabbits will there be in one year?”

这个数列是一,一,二,三,五,八,十三,从第三项起每一项都是前两项之和。Zhège shùliè shì yī, yī, èr, sān, wǔ, bā, shísān, cóng dì sān xiàng qǐ měi yī xiàng dōu shì qián liǎng xiàng zhī hé.  – This number sequence is one, one, two, three, five, eight, thirteen, and each term from the third term is the sum of the previous two terms.

向目葵种子和松果的螺线左旋和右旋的数量都是斐波那契数。Xiàng mù kuí zhǒngzǐ hé sōng guǒ de luó xiàn zuǒxuán hé yòu xuán de shùliàng dōu shì fěi bō nà qì shù.  – The number of left-handed and right-handed spirals of sunflower seeds and pine cones are both Fibonacci numbers.

百合花有三瓣花瓣,梅花有五瓣,向日葵有二十一或三十四瓣,雏菊有三十四,五十五和八十九三种数量的花瓣。Bǎihé huā yǒusān bàn huābàn, méihuā yǒu wǔ bàn, xiàngrìkuí yǒu èrshíyī huò sānshísì bàn, chújú yǒu sānshísì, wǔshíwǔ hé bāshíjiǔsān zhǒng shùliàng de huābàn. – Lilies have three petals, plums have five petals, sunflowers have twenty-one or thirty-four petals, and daisies have three types of petals: thirty-four, fifty-five and eighty-nine.

这些数字都符合斐波那契数列 | 如果把斐波那契数列中的数字 | 后一项除以前一项 | 随着数字的增多 | 这个比值越来越近于一点六一八零三 | 而一点六一八零三和我们熟悉的 | 黄金分割数关系密切 | 这些大自然与数字之间的神奇联系 | 又在向人类喑示着些什么呢?

Zhèxiē shùzì dōu fúhé fěi bō nà qì shùliè | rúguǒ bǎ fěi bō nà qì shùliè zhōng de shùzì | hòu yī xiàng chú yǐqián yī xiàng | suí zhāo shùzì de zēngduō | zhège bǐzhí yuè lái yuè jìn yú yī diǎn liùyībā líng sān | ér yī diǎn liùyībā líng sān hé wǒmen shúxī de | huángjīn fēngē shù guānxì mìqiè | zhèxiē dà zìrán yǔ shùzì zhī jiān de shénqí liánxì | yòu zài xiàng rénlèi yīn shìzhe xiē shénme ne?

– These numbers are all in line with the Fibonacci sequence | If the numbers in the Fibonacci sequence | divide the latter term by the former term | as the number increases | the ratio gets closer and closer to 1.61803| And 1.61803 is closely related to the familiar | golden ratio | these magical connections between nature and numbers | what is it showing to human beings?

所以如果当我们需要理解自然界的事情的时候我们第一个想的事情就是我们能不能将自然界的许多现象将它数学化。Suǒyǐ rúguǒ dāng wǒmen xūyào lǐjiě zìránjiè de shìqíng de shíhòu wǒmen dì yī gè xiǎng de shìqíng jiùshì wǒmen néng bùnéng jiāng zìránjiè de xǔduō xiànxiàng jiāng tā shùxué huà. – So if we need to understand things in nature, the first thing we think about is whether we can mathematically quantify many phenomena in nature.

数学就是这样 | 它其实彼此之间 | 也许可能都没有交集 | 然后(数学家)在做着一些 | 你无法理解甚至让数学家们互相之间 | 都无法理解的事情 | 但是他们的共性 | 我觉得都是在寻找规律 | 并且去解释现实中的问题。Shùxué jiùshì zhèyàng | tā qíshí bǐcǐ zhī jiān | yěxǔ kěnéng dōu méiyǒu jiāojí | ránhòu (shùxué jiā) zài zuòzhe yīxiē | nǐ wúfǎ lǐjiě shènzhì ràng shùxué jiāmen hù xiàng zhī jiān | dōu wúfǎ lǐjiě de shìqíng | dànshì tāmen de gòngxìng | wǒ juédé dōu shì zài xúnzhǎo guīlǜ | bìngqiě qù jiěshì xiànshí zhōng de wèntí. – That’s how mathematics is | it’s actually each other | maybe none of them intersect | and then (mathematicians) are doing something | things you can’t understand, even mathematicians from each other | I feel that we are all looking for the law | and to explain the problems in reality.

数学与音乐存在着某种惊人的共性。

毕达哥拉斯他把一根琴弦平均地分成。

二分之一段,三分之二段,四分之一段由此得出来这个世界的种谐的比例是一比二比三比四。

那么在这个过程里边我们就产生了我们声音里边最重要的四个音就是一四五一。

数学与音乐存在着某种惊人的共性。

毕达哥拉斯他把一根琴弦平均地分成。

二分之一段,三分之二段,四分之一段由此得出来这个世界的种谐的比例是一比二比三比四。

那么在这个过程里边我们就产生了我们声音里边最重要的四个音就是一四五一。

Shùxué yǔ yīnyuè cúnzàizhe mǒu zhǒng jīngrén de gòngxìng. Bì dá gē lā sī tā bǎ yī gēn qín xián píngjūn dì fēnchéng. Èr fēn zhī yī duàn, sān fēn zhī èr duàn, sì fēn zhī yī duàn yóu cǐ dé chūlái zhège shìjiè de zhǒng xié de bǐlì shì yī bǐ èr bǐ sān bǐ sì. Nàme zài zhège guòchéng lǐbian wǒmen jiù chǎnshēngle wǒmen shēngyīn lǐbian zuì zhòngyào de sì gè yīn jiùshì yīsìwǔyī.

– Mathematics and music have something surprising in common.

Pythagoras divided a string equally.

One-half, two-thirds, and one-quarter are derived from this, and the ratio of the species in this world is one to two to three to four.

Then in this process, we have produced the four most important tones in our voice, which are 1451.

古琴的十三个徵 | 它都是通过数学的这种计算而来的 | 所以来确定每一个音的音高 | 就是有效弦长的一比二处 | 所以来确定七徵的位置 | 那么其它的徵位 | 也是按照比例的不同 | 来确定它的位置。

Gǔqín de shísān gè zhǐ | tā dōu shì tōngguò shùxué de zhè zhǒng jìsuàn ér lái de | suǒyǐ lái quèdìng měi yīgè yīn de yīn gāo | jiùshì yǒuxiào xián zhǎng de yī bǐ èr chù | suǒyǐ lái quèdìng qī zhǐ de wèizhì | nàme qítā de zhǐ wèi | yěshì ànzhào bǐlì de bùtóng | lái quèdìng tā de wèizhì.

– The thirteen signs of the guqin | It is all calculated through mathematics | So to determine the pitch of each note | It is one to two of the effective string length | So to determine the position of the seven signs | Then other The sign | is also proportional to the difference | to determine its position.

音乐就是 sin 函数正弦函数因为它是波。

我们能够听到每一个音符的振动。

它就是不同的 sin 波那你不同的音乐里面。

对于你的音乐的组成本质上就是一堆正弦函的组成。

Yīnyuè jiùshì sin hánshù zhèngxián hánshù yīnwèi tā shì bō. Wǒmen nénggòu tīng dào měi yīgè yīnfú de zhèndòng. Tā jiùshì bùtóng de sin bō nà nǐ bùtóng de yīnyuè lǐmiàn. Duìyú nǐ de yīnyuè de zǔchéng běnzhí shàng jiùshì yī duī zhèngxián hán de zǔchéng.

– Music is a sin function sine function because it is a wave.

We can hear the vibration of each note.

It’s just the different sin waves that are in your different music.

The composition for your music is essentially the composition of a bunch of sine functions.

数学也伴随着西方绘画的演进。

文艺复兴期间很多艺术家和可科学家相信宇宙间的规律可以通几何原理明确地理性化。

因此很多艺术家同时也是数学家比如达 · 芬奇和丢勒画家弗朗切斯卡从几何原理中推导出透视画法从而使二维空问的画布可以展现二维的世界透视法改变了美术史。

十九世纪黎曼几何的出现把四维时空的概念带到美术界。

数学也伴随着西方绘画的演进。

文艺复兴期间很多艺术家和可科学家相信宇宙间的规律可以通几何原理明确地理性化。

Shùxué yě bànsuízhe xīfāng huìhuà de yǎnjìn. Wényì fùxīng qíjiān hěnduō yìshùjiā hàn kě kēxuéjiā xiāngxìn yǔzhòu jiān de guīlǜ kěyǐ tōng jǐhé yuánlǐ míngquè dìlǐ xìng huà. Yīncǐ hěnduō yìshùjiā tóngshí yěshì shùxué jiā bǐrú dá· fēn qí hé diū lēi huàjiā fú lǎng qiè sī kǎ cóng jǐhé yuánlǐ zhōng tuīdǎo chū tòushì huà fǎ cóng’ér shǐ èr wéi kōng wèn de huàbù kěyǐ zhǎnxiàn èr wéi de shìjiè tòushì fǎ gǎibiànle měishù shǐ. Shíjiǔ shìjì lí màn jǐhé de chūxiàn bǎ sìwéi shíkōng de gàiniàn dài dào měishù jiè.

– Mathematics also accompanied the evolution of Western painting.

During the Renaissance, many artists and scientists believed that the laws of the universe could be unambiguously geographicalized by the principles of geometry.

Therefore, many artists and mathematicians such as Leonardo da Vinci and Dürer painter Francesca derived perspective drawing from geometric principles, so that a two-dimensional canvas can show a two-dimensional world. Perspective changed the history of art. .

The emergence of Riemannian geometry in the nineteenth century brought the concept of four-dimensional space-time to the art world.

《阿维尼翁的少女》是毕加索的封神之作也是立体派绘画的开山之作。

毕加索把不同透视图在同一时间里展现出来。

这完全打破了传统的透视理论。

杜尚的名作 《下楼的裸女》把不同时间的人物形态定格在一个空间上而抽象派大师康定斯基则将绘画中的线条与色彩抽象为数学般简洁又神秘的形态。

简直把抽象的数学画了出来。

Ā wéiní wēng de shàonǚ” shì bìjiāsuǒ de fēng shén zhī zuò yěshì lìtǐ pài huìhuà de kāishān zhī zuò. Bìjiāsuǒ bǎ bùtóng tòushì tú zài tóngyī shíjiān lǐ zhǎnxiàn chūlái. Zhè wánquán dǎpòle chuántǒng de tòushì lǐlùn. Dù shàng de míngzuò “xià lóu de luǒnǚ” bǎ bùtóng shíjiān de rénwù xíngtài dìnggé zài yīgè kōngjiān shàng ér chōuxiàng pài dàshī kāngdìng sī jī zé jiāng huìhuà zhōng de xiàntiáo yǔ sècǎi chōuxiàng wéi shùxué bān jiǎnjié yòu shénmì de xíngtài. Jiǎnzhí bǎ chōuxiàng de shùxué huàle chūlái.

– „The Maiden of Avignon” is Picasso’s masterpiece and the pioneering work of Cubism.

Picasso showed different perspectives at the same time.

This completely breaks the traditional perspective theory.

Duchamp’s masterpiece „The Nude Descending Downstairs” fixed the forms of figures at different times in one space, while the abstract master Kandinsky abstracted the lines and colors in the painting into mathematically simple and mysterious forms.

It simply draws abstract mathematics.

音乐是最抽象的艺术。数学是最抽象的科学。绘画的潮流伴随着人们对时空的认识从这一点来说数学更像是艺术。

数学是什么?我们可以认为数学是人类文明 | 最核心最抽象的知识源泉。

Yīnyuè shì zuì chōuxiàng de yìshù. Shùxué shì zuì chōuxiàng de kēxué. Huìhuà de cháoliú bànsuízhe rénmen duì shíkōng de rènshí cóng zhè yīdiǎn lái shuō shùxué gèng xiàng shì yìshù. Shùxué shì shénme? Wǒmen kěyǐ rènwéi shùxué shì rénlèi wénmíng | zuì héxīn zuì chōuxiàng de zhīshì yuánquán.

– Music is the most abstract art. Mathematics is the most abstract science. The trend of painting is accompanied by people’s understanding of time and space. From this point of view, mathematics is more like art.

What is math? We can think that mathematics is the most core and abstract knowledge source of human civilization.

 

https://www.youtube.com/embed/BWfa8utRiPQ?start=0

 

 

出尔反尔 北约东扩让俄退无可退 |《中国新闻》CCTV中文国际

Chū’ěrfǎn’ěr běiyuē dōng kuò ràng é tuì wú kě tuì” |zhōngguó xīnwénCCTV zhōngwén guójì

– NATO’s eastward expansion leaves Russia „with no retreat” | „China News” CCTV Chinese International

 

中国新闻 Zhōngguó xīnwén – China News

 

出尔反尔 北约东扩让俄 退无可退Chū’ěrfǎn’ěr běiyuē dōng kuò ràng é tuì wú kě tuì”. – The eastward expansion of NATO has left Russia with „no retreat”.

切可行方案。Qiè kěxíng fāng’àn. – All feasible options.

美国使馆敦促美公民尽快离开乌克兰和俄罗斯。Měiguó shǐguǎn dūncù měi gōngmín jǐnkuài líkāi wūkèlán hé èluósī. – The U.S. embassy urged U.S. citizens to leave Ukraine and Russia as soon as possible.

沙特主储:将继遵守与俄罗斯等主要产油国先前达成的石油增产协议。Shātè zhǔ chǔ: Jiāng jì zūnshǒu yǔ èluósī děng zhǔyào chǎn yóu guó xiānqián dáchéng de shíyóu zēngchǎn xiéyì. – Saudi Arabia’s main reserve: Will continue to abide by the oil production increase agreement reached with major oil producers such as Russia.

沙特主储:将继遵守与俄罗斯等主要产油国先前达成的石油增产协议。Shātè zhǔ chǔ: Jiāng jì zūnshǒu yǔ èluósī děng zhǔyào chǎn yóu guó xiānqián dáchéng de shíyóu zēngchǎn xiéyì. – Saudi Arabia’s main reserve: Will continue to abide by the oil production increase agreement reached with major oil producers such as Russia.

朝中社报道朝鲜于2月27日进行了一次侦察卫星的发射试验。Cháo zhōng shè bàodào cháoxiǎn yú 2 yuè 27 rì jìnxíngle yīcì zhēnchá wèixīng de fǎ shè shìyàn. – North Korea conducted a test launch of a reconnaissance satellite on February 27, KCNA reported.

韩国2月新冠确诊病例累计新增200万例。Hánguó 2 yuè xīnguān quèzhěn bìnglì lěijì xīn zēng 200 wàn lì. – South Korea added 2 million new confirmed cases of new crown in February.

 

阿拉基

联合国前副秘书长

Ālā jī liánhéguó qián fù mìshū zhǎng

– Araki

former United Nations Under-Secretary-General

 

苏联曾得到北约不向东扩张的保证。Sūlián céng dédào běiyuē bù xiàng dōng kuòzhāng de bǎozhèng. – The Soviet Union had been assured that NATO would not expand eastward.

 

新西兰将取消对已接种疫苗的国际旅客抵新后自我隔离7天的要求。Xīnxīlán jiāng qǔxiāo duì yǐ jiēzhǒng yìmiáo de guójì lǚkè dǐ xīn hòu zìwǒ gélí 7 tiān de yāoqiú. – New Zealand will lift the requirement for vaccinated international travellers to self-isolate for seven days upon arrival.

 

但是东扩一直在持续 Dànshì dōng kuò yīzhí zài chíxù – But the eastward expansion has continued

北约的新成员国 Běiyuē de xīn chéngyuán guó  – new member of NATO

 

北约军演资科 Běiyuē jūn yǎn zī kē  – NATO Military Exercise Funding Section

已经与俄罗斯接壤 Yǐjīng yǔ èluósī jiērǎng  – already borders russia

澳大利亚东海岸连日来遭遇特续强降雨,截至2月28日累计造成,人丧生。Àodàlìyǎ dōng hǎi’àn liánrì lái zāoyù tè xù qiáng jiàngyǔ, jiézhì 2 yuè 28 rì lěijì zàochéng, rén sàngshēng. – The east coast of Australia has suffered from particularly heavy rainfall for the past few days.

 

我认为根本的解决办法就在欧洲国家手中。Wǒ rènwéi gēnběn de jiějué bànfǎ jiù zài ōuzhōu guójiā shǒuzhōng. – I think the fundamental solution is in the hands of European countries.

欧洲国家应该宣布。Ōuzhōu guójiā yīnggāi xuānbù. – European countries should announce.

联合国安理会对也门胡塞武装实施武器禁运。Liánhéguó ānlǐhuì duì yěmén hú sāi wǔzhuāng shíshī wǔqì jìn yùn. – UN Security Council imposes arms embargo on Yemen’s Houthis

北约不会吸纳乌克兰加入。Běiyuē bù huì xīnà wūkèlán jiārù. – NATO will not admit Ukraine to join.

乌克兰和北约联合军演资料 Wūkèlán hé běiyuē liánhé jūn yǎn zīliào – Ukrainian and NATO joint military exercises

现在只要说出来并落实到书面上。Xiànzài zhǐyào shuō chūlái bìng luòshí dào shūmiàn shàng. – Now just say it and put it into writing.

中美已建立五十队友好省州和二百三十三队友好城市关系。Zhōng měi yǐ jiànlì wǔshí duì yǒuhǎo shěng zhōu hé èrbǎi sānshísān duì yǒuhǎo chéngshì guānxì. – China and the United States have established 50 sister provinces and states and 233 sister cities.

签署一个国际协议事情就解决了 Qiānshǔ yīgè guójì xiéyì shìqíng jiù jiějuéle  – Sign an international agreement and things will be settled

中央援港防控专家组二月二十八日抵达香港。Zhōngyāng yuán gǎng fáng kòng zhuānjiā zǔ èr yuè èrshíbā rì dǐdá xiānggǎng. – The Central China-aided Hong Kong Prevention and Control Expert Team arrived in Hong Kong on February 28.

资料 Zīliào – material

二连浩特铁路口岸接运中欧班列突破五百列。Èrliánhàotè tiělù kǒu’àn jiē yùn zhōng’ōu bān liè túpò wǔbǎi liè. – The number of China-Europe freight trains connected to the Erenhot railway port exceeded 500.

高清 Gāoqīng  – HD

内蒙古呼和浩特:实行 四个一律 临时管控措施。Nèiménggǔ hūhéhàotè: Shíxíng sì gè yīlǜ línshí guǎnkòng cuòshī. – Hohhot, Inner Mongolia: Implement the „Four Uniforms” temporary control measures.

退役军人事务部与六家企业签署合作协议,拓展优待证使用场景。Tuìyì jūnrén shìwù bù yǔ liù jiā qì yè qiānshǔ hézuò xiéyì, tàzhǎn yōudài zhèng shǐyòng chǎngjǐng. – The Ministry of Veterans Affairs signed cooperation agreements with six companies to expand the use of preferential treatment cards.

如果德国能留在北约,并且北约可以在德国,保特驻军,那么北约将不会向东扩张,哪怕一英寸。Rúguǒ déguó néng liú zài běiyuē, bìngqiě běiyuē kěyǐ zài déguó, bǎo tè zhùjūn, nàme běiyuē jiāng bù huì xiàng dōng kuòzhāng, nǎpà yī yīngcùn. – If Germany can stay in NATO, and NATO can have troops in Germany, Botter, then NATO will not expand eastward even an inch.

工信部:二零二二年预计新建5G 基站六十万个以上。Gōngxìnbù: Èr líng èr’èr nián yùjì xīnjiàn 5G jīzhàn liùshí wàn gè yǐshàng. – Ministry of Industry and Information Technology: More than 600,000 new 5G base stations are expected to be built in 2022.

西方曾承不会让北约扩张---德国《明镜》周刊。Xīfāng céng chéng bù huì ràng běiyuē kuòzhāng–déguó míngjìng zhōukān. – The West has promised not to allow NATO to expand – Germany’s „Der Spiegel” weekly.

维利·维默尔 Wéi lì-wéi mò ěr – Willy Wimmer

交通运输部:二零二一年交通固定资产投资约三点六万亿元,同比增长百分之四。Jiāotōng yùnshū bù: Èr líng èryī nián jiāotōng gùdìng zīchǎn tóuzī yuē sān diǎn liù wàn yì yuán, tóngbǐ zēngzhǎng bǎi fēn zhī sì. – Ministry of Transport: In 2021, the investment in fixed assets in transport will be about 3.6 trillion yuan, a year-on-year increase of 4%.

泽连斯基签署乌克兰申请加入欧盟文件。Zé lián sī jī qiānshǔ wūkèlán shēnqǐng jiārù ōuméng wénjiàn. – Zelensky signs Ukraine’s application for EU membership.

北约问乌克兰提供反坦克武器和防空导弹。Běiyuē wèn wūkèlán tígōng fǎn tǎnkè wǔqì hé fángkōng dǎodàn. – NATO asked Ukraine to provide anti-tank weapons and anti-aircraft missiles.

北约成员国数量变化 Běiyuē chéngyuán guó shùliàng biànhuà  – Changes in the number of NATO members

冷战结束后加入的国家 lěngzhàn jiéshù hòu jiārù de guójiā – countries that joined after the cold war

俄国防部:俄战略导弹部队等开始战备值班。É guófáng bù: É zhànlüè dǎodàn bùduì děng kāishǐ zhànbèi zhíbān. – Russian Ministry of Defense: The Russian Strategic Missile Forces have begun combat readiness on duty.

欧盟和加拿大宣布对俄关闭领空。Ōuméng hé jiānádà xuānbù duì é guānbì lǐngkōng. – The European Union and Canada announced that they would close their airspace to Russia.

瑞士宣布参与欧盟对俄制裁。Ruìshì xuānbù cānyù ōuméng duì é zhìcái.  – Switzerland announces participation in EU sanctions against Russia.

俄罗斯对三十六个国家的航班关闭领空。Èluósī duì sānshíliù gè guójiā de hángbān guānbì lǐngkōng. – Russia closed its airspace to flights from 36 countries.

联合国大会二月二十八日就乌克兰局势召开紧急特别会议。Liánhéguó dàhuì èr yuè èrshíbā rì jiù wūkèlán júshì zhàokāi jǐnjí tèbié huìyì. – The United Nations General Assembly held an emergency special session on the situation in Ukraine on February 28.

俄罗斯金融市场二月二十八日出现大幅震荡,卢布汇率创历史新低。Èluósī jīnróng shìchǎng èr yuè èrshíbā rì chūxiàn dàfú zhèndàng, lúbù huìlǜ chuàng lìshǐ xīndī. – On February 28, the Russian financial market experienced great volatility, and the ruble exchange rate hit a record low.

俄罗斯央行二月二十八日宣布将基准利率提升至千分之二十。Èluósī yāngháng èr yuè èrshíbā rì xuānbù jiāng jīzhǔn lìlǜ tíshēng zhì qiān fēn zhī èrshí. – The Central Bank of Russia announced on February 28 that it would raise the benchmark interest rate to 20/1000.

中国驻乌克兰大使馆:二月二十八日中国开始从乌克兰撤出首批公民。Zhōngguó zhù wūkèlán dàshǐ guǎn: Èr yuè èrshíbā rì zhōngguó kāishǐ cóng wūkèlán chè chū shǒu pī gōngmín. – Chinese Embassy in Ukraine: On February 28, China began to withdraw its first citizens from Ukraine.

布林肯 Bù línkěn – Blinken

美国国务卿 Měiguó guówùqīng – U.S. Secretary of State

值得注意的是莫斯科在造谣。Zhídé zhùyì de shì mòsīkē zài zàoyáo. – It is worth noting that Moscow is spreading rumors.

称北约在冷战后承诺。Chēng běiyuē zài lěngzhàn hòu chéngnuò. – Called NATO’s post-Cold War commitments.

不接受东欧国家为北约成员国。Bù jiēshòu dōng’ōu guójiā wèi běiyuē chéngyuán guó. – Eastern European countries are not accepted as NATO members.

中国外交部:望各方给紧张局势降温,勿火上浇油。Zhōngguó wàijiāo bù: Wàng gè fāng gěi jǐnzhāng júshì jiàngwēn, wù huǒ shàng jiāo yóu. – Chinese Ministry of Foreign Affairs: I hope all parties will cool down the tension and not add fuel to the fire.

这些说法都是假的。Zhèxiē shuōfǎ dōu shì jiǎ de. – These claims are false.

中国外交部:研究协助在乌中国公民自愿安全撤离的一切可行方案。Zhōngguó wàijiāo bù: Yánjiū xiézhù zài wū zhōngguó gōngmín zìyuàn ānquán chèlí de yīqiè kěxíng fāng’àn. – Chinese Ministry of Foreign Affairs: Study all feasible options to assist the voluntary safe evacuation of Chinese citizens in Ukraine.

他们(北约)在二十世纪九十年代 Tāmen (běiyuē) zài èrshí shìjì jiǔshí niándài  – They (NATO) in the 1990s

普京 Pǔjīng  – Putin

俄罗斯总统 Èluósī zǒngtǒng – President of Russia

对我们承诺不会东扩 Duì wǒmen chéngnuò bù huì dōng kuò – Promise to us not to expand eastward

美国使馆敦促美公民尽快离开乌克兰和俄罗斯。Měiguó shǐguǎn dūncù měi gōngmín jǐnkuài líkāi wūkèlán hé èluósī. – The U.S. embassy urged U.S. citizens to leave Ukraine and Russia as soon as possible.

结果怎么样 Jiéguǒ zěnme yàng  – What’s the result

我们被骗了。Wǒmen bèi piànle. – We were deceived.

他们厚颜无耻地欺骗了我们。Tāmen hòuyánwúchǐ de qīpiànle wǒmen. – They brazenly lied to us.

北约东扩了五次 Běiyuē dōng kuòle wǔ cì – NATO expanded east five times

沙特王储:将继续遵守与俄罗斯等主要产油国先前达成的石油增产协议。Shātè wángchú: Jiāng jìxù zūnshǒu yǔ èluósī děng zhǔyào chǎn yóu guó xiānqián dáchéng de shíyóu zēngchǎn xiéyì. – Saudi crown prince: Will continue to abide by the oil production increase agreement reached with major oil producers such as Russia.

现在罗马尼亚波兰都部署了导弹系统。Xiànzài luómǎníyǎ bōlán dōu bùshǔle dǎodàn xìtǒng. – Now Romania and Poland have deployed missile systems.

这说明什么 Zhè shuōmíng shénme  – what does this mean

朝中社报道,朝鲜于二月二十七日进行了一次侦察卫星的发射试验。Cháo zhōng shè bàodào, cháoxiǎn yú èr yuè èrshíqī rì jìnxíngle yīcì zhēnchá wèixīng de fǎ shè shìyàn. – North Korea conducted a test launch of a reconnaissance satellite on February 27, KCNA reported.

不是我们在威胁别人。Bùshì wǒmen zài wēixié biérén. – It’s not that we are threatening others.

韩国二月新冠确诊病例累计新增二百万例。Hánguó èr yuè xīnguān quèzhěn bìnglì lěijì xīn zēng èrbǎi wàn lì. – South Korea added 2 million new confirmed cases of new crown in February.

我们没去美国边境没去英国边境。Wǒmen méi qù měiguó biānjìng méi qù yīngguó biānjìng. – We didn’t go to the US border, we didn’t go to the UK border.

是他们来找我们了。Shì tāmen lái zhǎo wǒmenle. – It was they who came to us.

现在他们又说乌克兰也要加入北约。Xiànzài tāmen yòu shuō wūkèlán yě yào jiārù běiyuē. – Now they say Ukraine is also joining NATO.

新西兰将取消对已接种疫苗的国际旅客抵新后自我隔离七天的要求。Xīnxīlán jiāng qǔxiāo duì yǐ jiēzhǒng yìmiáo de guójì lǚkè dǐ xīn hòu zìwǒ gélí qītiān de yāoqiú. – New Zealand will lift the requirement for vaccinated international travellers to self-isolate for seven days upon arrival.

 

https://www.youtube.com/embed/1mup_Dn70wI?start=00