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Frey showed how starting with a fictitious solution to Fermat's last equation
弗萊展示出如何從費馬最后定理的一個假定解著手，
if such a horrible, beast existed, he could make an elliptic curve with some very weird properties.
如果這樣一個可怕的怪獸確實存在，他就可賦予橢圓曲線一些非常怪異的特性。
That elliptic curve seems to be not modular,
那種橢圓曲線看來并非模形式，
but Shimura-Taniyama says that every elliptic curve is modular.
但谷山-志村猜想認為每條橢圓曲線就是模形式的。
So if there is a solution to this equation it creates such a weird elliptic curve, it defies Taniyama- Shimura.
因此如果這個等式有解，就會產生如此這般怪異的橢圓曲線，而不遵從谷山-志村猜想。
So in other words, if Fermat is false, so is Shimura-Taniyama,
換而言之，如果費馬是錯的，谷山-志村猜想也就是錯的，
or said differently, if Shimura- Taniyama is correct, so is Fermat's last theorem.
或者說如果谷山-志村猜想是對的，那么費馬最后定理也是對的。
Fermat and Taniyama-Shimura were now linked, apart from just one thing.
費馬和谷山-志村現已聯系在一起，只除了一件事。
The problem is that Frey didn't really prove that his elliptic curve was not modular.
問題在于弗萊其實沒有證明他的橢圓曲線不是模形式
He gave a plausibility argument which he hoped could be filled in by experts, and then the experts started working on it.
他給出了一個看似有理的論點，寄希望于專家們能夠證實，于是專家們開始進行研究。
In theory, you could prove Fermat by proving Taniyama, but only if Frey was right.
理論上，你可經由證實谷山來證實費馬，但只有在弗萊正確時。
Frey's idea became known as the epsilon conjecture and everyone tried to check it.
弗萊的觀點得名為"Epsilon猜想"，大家都試圖要驗證它。
One year later, in San Francisco, there was a breakthrough.
一年之后，在舊金山市有了個突破。
