纪录片《费马最后的定理》 第13期 提出Epsilon猜想（在线收听）

Frey showed how starting with a fictitious solution to Fermat's last equation

弗莱展示出如何从费马最后定理的一个假定解着手，

if such a horrible, beast existed, he could make an elliptic curve with some very weird properties.

如果这样一个可怕的怪兽确实存在，他就可赋予椭圆曲线一些非常怪异的特性。

That elliptic curve seems to be not modular,

那种椭圆曲线看来并非模形式，

but Shimura-Taniyama says that every elliptic curve is modular.

但谷山-志村猜想认为每条椭圆曲线就是模形式的。

So if there is a solution to this equation it creates such a weird elliptic curve, it defies Taniyama- Shimura.

因此如果这个等式有解，就会产生如此这般怪异的椭圆曲线，而不遵从谷山-志村猜想。

So in other words, if Fermat is false, so is Shimura-Taniyama,

换而言之，如果费马是错的，谷山-志村猜想也就是错的，

or said differently, if Shimura- Taniyama is correct, so is Fermat's last theorem.

或者说如果谷山-志村猜想是对的，那么费马最后定理也是对的。

Fermat and Taniyama-Shimura were now linked, apart from just one thing.

费马和谷山-志村现已联系在一起，只除了一件事。

The problem is that Frey didn't really prove that his elliptic curve was not modular.

问题在于弗莱其实没有证明他的椭圆曲线不是模形式

He gave a plausibility argument which he hoped could be filled in by experts, and then the experts started working on it.

他给出了一个看似有理的论点，寄希望于专家们能够证实，于是专家们开始进行研究。

In theory, you could prove Fermat by proving Taniyama, but only if Frey was right.

理论上，你可经由证实谷山来证实费马，但只有在弗莱正确时。

Frey's idea became known as the epsilon conjecture and everyone tried to check it.

弗莱的观点得名为"Epsilon猜想"，大家都试图要验证它。

One year later, in San Francisco, there was a breakthrough.

一年之后，在旧金山市有了个突破。