纪录片《费马最后的定理》 第10期 谷山-志村猜想（在线收听）

In 1955 there was an international symposium and Taniyama posed two or three problems.

在1955年的一次国际学术报告会上，谷山丰提出了两三个问题。

The problems posed by Taniyama led to the extraordinary claim that

谷山丰提的问题引致的非凡声明即为

every elliptic curve was really a modular form in disguise.

每条椭圆曲线实为改头换面的模形式

It became known as the Taniyama-Shimura conjecture.

这就是有名的'谷山-志村猜想'

The Taniyama-Shimura conjecture says, that every rational elliptic curve is modular and that's so hard to explain.

谷山-志村猜想是说，每条合理的椭圆曲线都是模，很难来说清楚。

So let me explain. Over here you have the elliptic world, the elliptic curve, these doughnuts,

让我来解释一下。这儿有个椭圆世界，椭圆曲线，这些甜甜圈，

and over here you have the modular world, modular forms with their many, many symmetries.

而这儿有个模世界，模形式以及它们许多许多的对称形式。

The Shirmura-Taniyama conjecture makes a bridge between these two worlds.

谷山-志村猜想在这两个世界间架起了一座桥梁。

These worlds live on different planets.

这两个世界是在不同的星球上。

It's a bridge, it's more than a bridge, it's really a dictionary,

它是座桥，又不仅是座桥，它实际上还是本字典，

a dictionary where questions, intuitions, insights, theorems in the one world,

这本字典中一个世界中的问题、直觉、见地、定理，

get translated to questions, intuitions in the other world.

翻译成为另一个世界中的问题、直觉。