纪录片《费马最后的定理》 第06期 数学证明

（单词翻译）

Well how many numbers are there to beat that with?

要这么做的话得要试多少个数?

You've got to do it for infinitely¹ many numbers.

你得要这么试上无穷无尽的数字

So after you've done it for one, how much closer have you got?

那么你试了一个数后，距离目标还有多远?

Well there's still infinitely many left.

仍有不可计数的那些

After you've done it for 1,000 numbers, how many, how much closer have you got?

在你试了1千个数后，还有多少，距离目标还有多远?

After you've done a few million, there's still infinitely many left.

就算你试了数百万个以后，还是有无穷无尽的。

In fact, you haven't done very many have you?

事实上，你没试多少，对吧?

A computer can never check every number. Instead, what's needed is a mathematical proof.

计算机从来不能把每个数字都试一遍。相反，所需的是数学证明。

A mathematician² is not happy until the proof is complete and considered complete by the standards of mathematics.

除非证明过程完整，而且就数学标准看来是完整的，不然数学家是不会高兴的。

In mathematics there's the concept of proving something, of knowing it with absolute certainty.

数学世界中的概念是要证明某样东西，要绝对确定地了解它。

Which, well it's called rigorous proof.

而这被称为铁证

Well, that's what mathethematics it's all about

数学就是那么回事

A prove it's a sort of reason, it explains why no numbers fit the equation without having to check every number

证明是一种论据，它解释了为何没有数字符合那个等式，而用不着查验每个数字。

After centuries of faling to have a prove

历经数世纪寻求证明的失败

mathematicians³ began to abandon Fermat in favor of more serious math

数学家们开始撇开费马而转向更严肃的数学。