纪录片《费马最后的定理》 第09期 关于模形式

Together, Taniyama and Shimura worked on the complex mathematics of modular functions.

谷山丰和志村五郎一起进行模函数方面复杂数学的研究

I really can't explain what a modular function is in one sentence.

我实在不能用一句话来描述模函数是什么

I can try and give you a few sentences to explain it.

我可以试着以几句话来解释

I really can't put it in one sentence.

确实不能以一句概括之

Oh it's impossible.

哦，不可能的。

There's a saying attributed to Eichler that there are five fundamental operations of arithmetic:

埃其勒曾说过算术中有五种基本运算:

addition, subtraction¹, multiplication², division and modular forms.

加，减，乘，除以及模形式。

Modular forms are functions on the complex plane that are inordinately³ symmetric.

模形式是有着非比寻常对称性的复杂平面的函数

They satisfy so many internal symmetries that their mere⁴ existence seem like accidents, but they do exist.

它们具有如此多的内在对称性，其存在看来像出自意外，但它们确实存在。

This image is merely a shadow of a modular form.

这幅图像仅是一个模形式的映射

To see one properly your TV screen would have to be stretched into something called hyperbolic space.

要看得真切，你的电视屏可能得需要伸展入双曲空间。

Bizarre modular forms seem to have nothing whatsoever⁵ to do with the humdrum⁶ world of elliptic curves.

怪里怪气的模形式看上去和椭圆曲线的单调世界没什么关系。

But what Taniyama and Shimura suggested shocked everyone.

但谷山丰和志村五郎的提法语惊四座。

1 subtraction   

n.减法，减去

参考例句：

• We do addition and subtraction in arithmetic.在算术里,我们作加减运算。
• They made a subtraction of 50 dollars from my salary.他们从我的薪水里扣除了五十美元。

2 multiplication   

n.增加，增多，倍增；增殖，繁殖；乘法

参考例句：

• Our teacher used to drum our multiplication tables into us.我们老师过去老是让我们反覆背诵乘法表。
• The multiplication of numbers has made our club building too small.会员的增加使得我们的俱乐部拥挤不堪。

3 inordinately   

adv.无度地，非常地

参考例句：

• But if you are determined to accumulate wealth, it isn't inordinately difficult. 不过，如果你下决心要积累财富，事情也不是太难。 来自互联网
• She was inordinately smart. 她非常聪明。 来自互联网

4 mere   

adj.纯粹的；仅仅，只不过

参考例句：

• That is a mere repetition of what you said before.那不过是重复了你以前讲的话。
• It's a mere waste of time waiting any longer.再等下去纯粹是浪费时间。

5 whatsoever   

adv.（用于否定句中以加强语气）任何；pron.无论什么

参考例句：

• There's no reason whatsoever to turn down this suggestion.没有任何理由拒绝这个建议。
• All things whatsoever ye would that men should do to you,do ye even so to them.你想别人对你怎样，你就怎样对人。

6 humdrum   

adj.单调的，乏味的

参考例句：

• Their lives consist of the humdrum activities of everyday existence.他们的生活由日常生存的平凡活动所构成。
• The accountant said it was the most humdrum day that she had ever passed.会计师说这是她所度过的最无聊的一天。