纪录片《费马最后的定理》 第21期 转换思维（在线收听）

But there was still a problem.

但仍存有一个问题。

Late in the spring of '93 I was in this very awkward position

93年的暮春时分，我处于一个非常尴尬的境地，

and I thought I'd got most of the curves to be modular,

我认为我已将大多数的曲线化为模形式，

so that was nearly enough to be content to have Fermat's last theorem,

那对于证明费马最后定理来说已几近足够，

but there was this, these few families of elliptic curves that had escaped the net.

但情况是，有少数椭圆曲线族仍无法纳入证明体系。

I was sitting here at my desk in May of '93, still wondering about this problem,

93年的5月，我就坐在书桌这儿，仍在考虑这个难题，

and I was casually glancing at a paper of Barry Mazur's

而我无意间瞥见了巴里·梅休尔的一篇论文，

and there was just one sentence which made a reference to actually what's a 19th-century construction

其中只有一句话提及的实为19世纪时期的一个结构，

and I just instantly realised that there was a trick that I could use,

我当即意识到其中有个技巧我可以用上，

that I could switch from the families of elliptic curves I'd been using.

我可以将我正在使用的椭圆曲线族进行转换

I'd been studying them using the prime three, I could switch and study them using the prime five.

以前是在用质数3来研究它们，我可以进行转换，用质数5来研究它们。

It looked more complicated, but I could switch from these awkward curves that I couldn't prove were modular,

看起来是更复杂了，但我可以对这些棘手的我还不能证明其为模形式的曲线进行转换

to a different set of curves which I'd already proved were modular

转为我已证明为模形式的另一种曲线族，

and use that information to just go that one last step.

而且利用那信息来迈出最后一步。

I just kept working out the details, time went by and I forgot to go down to lunch.

我一直在钻研细节，时间过去了，我忘记了下楼吃午饭。

It got to about teatime, I went down and Nada was very surprised that I'd arrived so late

到了下午茶时间，我下楼来，娜达非常惊讶我来得这么晚，

and then I told her that I, I believed I'd solved Fermat's last theorem.

于是我告诉她，我相信我已经破解了费马最后定理。