《环球数学圈》前9分钟“字幕”

今天获悉姜萍事件尘埃落地，作为业余数学爱好新手村老牙齿，我只能心疼姜萍。特此推荐纪录片《环球数学圈》Math Circles Around the World (2021)，让更多人看看在柏林、伯克利、莫斯科的数学圈的样子。同时希望咱们本土的数学圈对业余数学爱好者多一些宽容。

DGD网站是合法的观影通道在

https://www.discretization.de/movies/9/

通义AI音频转文字并翻译。大概一开始选择的是英语语音，因此德语发音、俄语发音转不成，我按视频上的英文字母整理。视频上说英语时，无字幕。

字幕及译文渣，勿喷。有兴趣一起来捉虫、勘误。

后续的字幕整理工作，我没有计划，或许明年下半年再继续。若有谁有兴趣接力做字幕整理，我可以分享影片录屏视频。

（一）

序幕亮相，柏林、伯克利、莫斯科的三个数学圈。

在柏林

Prof.Bobenko 00:06

You get the problems and you have one hour to solve them.

你们拿到问题。你们有一个小时解决问题。

Prof.Bobenko 00:14

Simply not well known that one can do such things in mathematics. I think we should give our children a chance, really, to enjoy real mathematics and to be competitive.

人们根本不知道在数学中可以做这样的事情。我认为我们应该给孩子们一个机会，真正地去享受真正的数学和竞争。

在伯克利

Prof.Stankova 00:28

Now, let's go back to our problem and look at it with different eyes. Mathematics teaches you to see the big picture. Mathematics teaches you about the connections between different objects. They don't have to be just mathematical; They could be anything in science or anything in life. But mathematics is the pedagogical glue that puts things together.

现在，让我们回到我们的问题，用不同的眼光来看待它。数学教你看到大局。数学教你不同物体之间的联系。它们不必只是数学的，它们可以是科学或生活中的任何东西。但数学是将事物联系在一起的教学粘合剂。

Arina and Yakov 00:54

Quantum mechanics is just, yeah, I don't know, linear algebra, Yeah, but I don't know it yet.

量子力学只是，是的，我不知道，线性代数，是的，但我还不知道。

在莫斯科

Dr. Yashchenko 01:04

Math circle is a team work. You will have fun from your first solutions.

数学圈是团队协作。你会从你率先解答中获得喜悦。

Prof.Bobenko 01:13

So I come from this system has influenced my life. I want them to become mathematicians.

所以我来自这个系统影响了我的生活。我希望他们成为数学家。

（二）

在伯克利

Prof.Stankova 01:27

It's the best place in the world for any activity like this. There is an influx of immigrants from many different countries, especially from Eastern Europe. And here we are with 500 students in a dozen sessions, from 30, 35 students in only one classroom for a kid in us to sacrifice 2 hours every week, it's a big deal. So this is a huge area, a trip to the math circle for some kids could last as long, 6 hours every week. In Eastern Europe, kids went to the man's circle because they loved so much what was happening in school, they wanted more of it. Here, kids come to the math circle very often for exactly the opposite reason. They dislike what's happening in school and they want something different.

它是世界上进行任何此类活动的最佳场所。来自许多不同国家的移民涌入，尤其是来自东欧的移民。在这里，我们有十几个课程中的500名学生，从30到35名学生中，仅在一个教室里，我们的一个孩子每周牺牲2个小时，这是一件大事。所以这是一个很大的地区，对一些孩子来说，去数学圈的通勤时间可能会很长。在东欧，每周6个小时，孩子们去数学圈是因为他们非常喜欢学校里发生的事情，他们想要更多的东西。在这里，孩子们经常因为完全相反的原因来数学圈。他们不喜欢学校里发生的事情，他们想要一些不同的东西。

门口对话 02:23

Hello, are you for the math circle? Which group are you in? I’m in Beginners 1. Wherever you go, you need math. Really, even just buying a house, if you want to rent an apartment, there's a lot of math and just doing that, are you also going the Math circle? What is your name? Liam.

你好，你是来参加数学圈的吗？你在哪一组？我在初学者1组。无论你去哪里，你都需要数学。真的，即使只是买房子，如果你想租一套公寓，有很多数学问题，只是这样做，你也会去数学圈吗？你叫什么名字？利亚姆。

课堂 02:41

Good evening everyone. Good evening Sense. You guys giving me homework? I suggest we start with number 9. Who would like to write the solution to 9 on the board? Ethan and Liam, go ahead. I mean, the question is to find the bottom square, none of the same two numbers can be in any row or any column, that has to be like all different numbers between 1, 2, 3, and 4.

大家晚上好！老师好！你们给我布置作业？我建议我们从数字9开始。谁想在黑板上写9的解决方案？伊森和利亚姆，继续吧。我的意思是，问题是找到底方格，任何行或任何列中都不能有相同的两个数字，那必须像1、2、3和4之间的所有不同数字一样。

发言人 03:14

All right, so what do we do? How do we find that mysterious number? This side would be 3 because there's a 4 here and there's a 3 here, this is a …

好的，那我们该怎么办？我们如何找到那个神秘的数字？这一侧填3，因为这里个4，这里有个3，这是一个……

Prof.Stankova 03:29

Liam help. 利亚姆来试试。

Liam 03:30

This would be, well, this would be a 4 because 2 can't go here because there's a 2 there and 4 can't go there because there's a 4 there. And then figure to figure this out. Well, no, that this is a 3 and this is a 4. And because 2, 3 and 4 are already used here, this has to be 1. And then if these numbers are 3, 1, and 4, we know that the answer has to be 2.

这填4，因为2不能去这里，因为那里有2，4不能去那里，因为那里有4。然后想办法解决这个问题。好吧，不，这是3，这是4。因为这里已经使用了2、3和4，所以这必须是一个。如果这些数字是3、1和4，我们就知道答案必须是2。

老师：

And you actually completed the rest of the table. Do you know why it is important to fill in the rest of the table?

你实际上完成了（幻方？）格子的其余部分。你知道为什么填写格子的其余部分很重要吗？

Prof.Stankova 04:01

Now for homework, I want you to create your own problem 4 by 4. And if you want 5 by 5, put as few numbers as possible. That would still make the solution unique.

现在家庭作业，我希望你创建自己的问题4×4。如果你想要5×5，请输入尽可能少的数字。这仍然会使解决方案独一无二。

Prof.Stankova 04:30

One of the questions that I love asking them every year is, what is your favorite problem that you can solve stated? Explain to us why it is your favorite problem and solve it. And the other favorite question that I have is what is your favorite problem that you can not yet solve? Explain why you would like to solve it, but why you can not yet solve it.

我每年都喜欢问他们的一个问题是，你最喜欢解决的问题是什么？向我们解释为什么这是您最喜欢的问题并解决它。我最喜欢的另一个问题是什么是你最喜欢的问题，但你还不能解决？解释为什么你想解决它，但为什么你还不能解决它。

（三） 在柏林

Berlin

Technical University

Prof.Bobenko 05:17

Mathematical Circle is a sort of research for school people. They get problems and it's not quite clear how to solve them. So you should come up with some idea.

数学圈是面向学生的一种研究。他们遇到问题，但不清楚如何解决。所以你应该想出一些主意。

英文字幕 05:28

They meet each other here. Yeah, they have to.

它们在这里相遇。是，那必须的。

发言人 05:35

They come to a math circle to enjoy mathematics.

他们来到数学圈享受数学的愉悦。

Prof. Suris 05:41

They have to be slightly crazy for mathematics, slightly mad, because they are going to invest time into something which is not very fashionable in this society.

他们来到一个月的圈子来享受数学。他们必须对数学有点疯狂，有点疯狂，因为他们要把时间投入到这个社会不太流行的东西上。

英文字幕

Prof.Bobenko 05:53

We had an unusual homework for today. You had to bring your favorite problems for us to solve. OK. Who is the first one?

今天的回家作业不寻常。你得带来你最喜欢的问题，让大家解决。OK，谁先来？

学生甲 06:08

It’s a logical problem. There are 24 monks, they don’t speak to each other because they meditate a lot. So they don’t communicate. But they all know that an illness has broken out. And you recognize it only by a point on a forehead which you of course can’t see, there are no mirrors. All you know that at least one is ill. After 7 days all the ill monks go to the hospital. How many ill monks there are?

这是道逻辑问题。有 24 名僧侣，他们彼此不说话，因为他们经常打坐。所以他们不沟通。但他们都知道，疾病爆发了。你只能通过额头上的一个点来识别它，你当然看不到它，没有镜子。你只知道至少有一个人生病了。7 天后，所有生病的僧侣都去了医院。有多少生病的僧侣？

英文字幕

Prof.Bobenko 06:57

Have you understood the problem?

你们理解这个问题么？

学生乙

Won’t you say how they get ill?

你不说说他们是怎么生病的吗？

学生丙

They know that no one will get ill anymore, and they are all thinking logically.

他们知道没有人会再生病了，他们都在用逻辑来思考。

学生乙

When two are ill, the first one sees that the other one ill. He is not sure about himself, but he sees another ill person. And knows that he is also ill.

当两个人生病时，第一个人看到另一个人生病了。他对自己不确定，但他看到了另一个病人。并且知道他也生病了。

学生丁

No, he doesn’t know that two persons are ill.

不，他不知道那两人都病了。

学生乙

Shut up and listen to me!

安静！听我说。

学生丙

They see on the second day that no one went to the hospital on the first day.

他们在第二天看到第一天没有人去医院。

学生甲

There was only one chance to go to the hospital on each of the days. They notice whether someone has left or not.

每天只有一次去医院的机会。他们注意到是否有人离开了。

Prof.Bobenko 07:42

All the monks are thinking logically. It’s an important point. There are not 24 monks, there are 24 mathematicians I would say. Our next topic is about inscribed polyhedral. I suggest we go down to our 3D cave. And we will look at different polyhedral.

所有僧侣都讲逻辑。这是要点。与其说是24个僧侣在思考，不如说是24个数学家在思考。我们的下一个主题是关于内切多面体。我建议我们去我们的 3D 洞穴。我们将研究不同的多面体。

Prof.Bobenko 08:18

Can you see something special in the circles?

在这些圈圈内部，你们看到有啥特别之处？

学生某某某

They touch each other. Exactly on this point. It doesn’t intersect the circle.

它们互相接触。就在这一点上。它不会与圆相交。

Prof.Bobenko

Exactly, here is the edge. We are inside the sphere. Here you see the same from the outside. This is not a platonic solid. There are not so many symmetries here, but all the edges touch the sphere.

没错，这就是边。我们在球体内部。在这里，你可以从外面看到同样的情况。这不是柏拉图多面体。这里没有那么多对称性，但所有的边都接触了球体。

Prof.Bobenko 08:52

The first mathematical circle, has started long time ago in the 30s in the Soviet Union. This was something special. What has started in Russia?

第一个数学圈，在苏联很久以前就开始了，在1930年代。这是一件特别的事情。俄罗斯开始了什么？