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Andrew was embarking on one of the most complex calculations in history.
安德魯要進行的是史上最為復雜的計算之一。
For the first two years, he did nothing but immerse himself in the problem, trying to find a strategy which might work.
在頭兩年，他其它的事什么都沒做，只是埋首于難題當中，試圖找到有用的策略。
So it was now known that Taniyama-Shimura implied Fermat's last theorem.
現(xiàn)在已經(jīng)知道谷山-志村猜想暗示了費馬最后定理。
What does Taniyama-Shimura say?
谷山-志村猜想是怎么說的?
It says that all elliptic curves should be modular.
它說所有的橢圓曲線都應為模形式
Well this was an old problem, been around for 20 years and lots of people would try to solve it.
這是個老難題了，已有20年左右，許多人嘗試解決它。
Now one way of looking at it is that you have all elliptic curves and then you have the modular elliptic curves
而如今看待它的一種方式就是，你有了所有的橢圓曲線，接著你又有了模形式橢圓曲線，
and you want to prove that there are the same number of each.
你所要證明的就是這兩者有同樣的數(shù)量。
Now of course you're talking about infinite sets, so you can't just can't count them per say,
當然了，所談及的是無限集合，因此當然不能僅靠計數(shù)，
but you can divide them into packets and you could try to count each packet and see how things gone
但你可將它們分成一族族的，這樣就可盡量來數(shù)每個族，看看會如何，
and this proves to be a very attractive idea for about 30 seconds
頭30秒這是個相當吸引人的想法
but you can't really get much further than that,
但其實你也只能到那一地步了
and the big question on the subject was how you could possibly count, and in fact, Wiles introduced the correct technique.
而關(guān)于這個的關(guān)鍵問題在于你如何來計數(shù)，實際上，懷爾斯引入了正確的方法。
Andrew's trick was to transform the elliptic curves into something called Galois representations which would make counting easier.
安德魯?shù)姆椒ㄊ菍E圓曲線轉(zhuǎn)化為稱為伽羅華表示的形式，這能使計數(shù)容易些。
Now it was a question of comparing modular forms with Galois representations, not elliptic curves.
現(xiàn)在是將模形式和伽羅華表示、而不是和橢圓曲線進行比較的問題了。
