纪录片《费马最后的定理》 第17期 伊娃沙娃理论

（单词翻译）

Now you might ask and it's an obvious question,

你可能会问，也是个显而易见的问题，就是：

why can't you do this with elliptic curves and modular forms,

为什么你不可以用椭圆曲线和模形式来进行

why couldn't you count elliptic curves, count modular forms, show they're the same number?

为什么你不可以数椭圆曲线、数模形式，再表示它们一样多?

Well, the answer is people tried and they never found a way of counting,

答案就在于人们试过了，但从未能找到一种计数的方式，

and this was why this is the key breakthrough,

这即为关键突破所在的原因

that I found a way to count not the original problem, but the modified problem.

我找到的方式不是来计数原问题，而是修改后的问题。

I found a way to count modular forms and Galoisrepresentations.

我找到了一种计数模形式和伽罗华表示的方法。

This is only the first step and have already taken 3 years of Andrew's life.

这只是第一步，但已花费了安德鲁三年的时间。

My wife's only known me while I've been working on Fermat.

我太太只知道我在研究费马定理。

I told her a few days after we got married.

结婚后数天我告诉她的。

I decided¹ that I really only had time for my problem and my family.

我决定把我仅有时间用于我的课题和我的家庭。

So I'd found this wonderful counting mechanism²

因此我找到了这个很棒的计数机理，

and I started thinking about this concrete problem in terms of Iwasawa theory.

并开始从伊娃沙娃理论的角度来考虑这个具体问题。

Iwasawa theory was the subject I'd studied as a graduate student

伊娃沙娃理论是我做为研究生时的课题，

and in fact with my advisor³, John Coates, I'd used it to analyse elliptic curves.

实际上我正要和我的导师约翰·科茨来将其用在分析椭圆曲线上。