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In 1955 there was an international symposium and Taniyama posed two or three problems.
在1955年的一次國際學術報告會上，谷山豐提出了兩三個問題。
The problems posed by Taniyama led to the extraordinary claim that
谷山豐提的問題引致的非凡聲明即為
every elliptic curve was really a modular form in disguise.
每條橢圓曲線實為改頭換面的模形式
It became known as the Taniyama-Shimura conjecture.
這就是有名的'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-志村猜想是說，每條合理的橢圓曲線都是模，很難來說清楚。
So let me explain. Over here you have the elliptic world, the elliptic curve, these doughnuts,
讓我來解釋一下。這兒有個橢圓世界，橢圓曲線，這些甜甜圈，
and over here you have the modular world, modular forms with their many, many symmetries.
而這兒有個模世界，模形式以及它們許多許多的對稱形式。
The Shirmura-Taniyama conjecture makes a bridge between these two worlds.
谷山-志村猜想在這兩個世界間架起了一座橋梁。
These worlds live on different planets.
這兩個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,
它是座橋，又不僅是座橋，它實際上還是本字典，
a dictionary where questions, intuitions, insights, theorems in the one world,
這本字典中一個世界中的問題、直覺、見地、定理，
get translated to questions, intuitions in the other world.
翻譯成為另一個世界中的問題、直覺。
