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本片从证明了费玛最后定理的安德鲁·怀尔斯开始谈起，描述了费玛最后定理的历史始末。
n. 战略，策略
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- Andrew was embarking on one of the most complex calculations in history.
- 安德鲁要进行的是史上最为复杂的计算之一。
- For the first two years, he did nothing but immerse himself in the problem, trying to find a strategy which might work.
- 在头两年，他其它的事什么都没做，只是埋首于难题当中，试图找到有用的策略。
- So it was now known that Taniyama-Shimura implied Fermat's last theorem.
- 现在已经知道谷山-志村猜想暗示了费马最后定理。
- What does Taniyama-Shimura say?
- 谷山-志村猜想是怎么说的?
- It says that all elliptic curves should be modular.
- 它说所有的椭圆曲线都应为模形式
- Well this was an old problem, been around for 20 years and lots of people would try to solve it.
- 这是个老难题了，已有20年左右，许多人尝试解决它。
- Now one way of looking at it is that you have all elliptic curves and then you have the modular elliptic curves
- 而如今看待它的一种方式就是，你有了所有的椭圆曲线，接着你又有了模形式椭圆曲线，
- and you want to prove that there are the same number of each.
- 你所要证明的就是这两者有同样的数量。
- Now of course you're talking about infinite sets, so you can't just can't count them per say,
- 当然了，所谈及的是无限集合，因此当然不能仅靠计数，
- but you can divide them into packets and you could try to count each packet and see how things gone
- 但你可将它们分成一族族的，这样就可尽量来数每个族，看看会如何，
- and this proves to be a very attractive idea for about 30 seconds
- 头30秒这是个相当吸引人的想法
- but you can't really get much further than that,
- 但其实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.
- 而关于这个的关键问题在于你如何来计数，实际上，怀尔斯引入了正确的方法。
- Andrew's trick was to transform the elliptic curves into something called Galois representations which would make counting easier.
- 安德鲁的方法是将椭圆曲线转化为称为伽罗华表示的形式，这能使计数容易些。
- Now it was a question of comparing modular forms with Galois representations, not elliptic curves.
- 现在是将模形式和伽罗华表示、而不是和椭圆曲线进行比较的问题了。
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