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It looks so simple yet the complexity, especially arithmetic complexity, is immense.
它看來如此簡單，然而其復雜性，尤其是幾何復雜性，極大。
Every point on the doughnut is the solution to an equation.
甜甜圈上的每個點都是某個等式的解。
Andrew Walis now studied these elliptic equations and set aside his dream.
安德魯·懷爾斯現正在研究這些橢圓等式，而將他的夢想置于一旁。
What he didn't realise was that on the other side of the world
他未意識到的是在地球的另一邊，
elliptic curves and Fermat's last theorem were becoming inextricably linked.
橢圓曲線和費馬最后定理不可避免地聯系在了一起。
I entered the University of Tokyo in 1949 and that was four years after the War,
我于1949年進入東京大學，那是二戰結束后四年，
but almost all professors were tired and the lectures were not inspiring.
但幾乎所有的教授都精疲力竭，而且講學也不吸引人。
Goro Shimura and his fellow students had to rely on each other for inspiration.
志村五郎和他的學生只能靠他們自己之間互相激勵。
In particular, he formed a remarkable partnership with a young man by the name of Utaka Taniyama.
尤其是，他與一個名為谷山豐的年輕人結成了非凡的伙伴關系。
That was when I became very close to Taniyama.
正是那時，我開始與谷山豐變得非常親密
Taniyama was not a very careful person as a mathematician.
作為一名數學家，谷山豐不是個很仔細的人。
He made a lot of mistakes, but he made mistakes in a good direction,
他犯了很多錯，但他所犯的錯大方向是對的，
and so eventually he got right answers and I tried to imitate him,
因此最終他得到了正確的答案，我嘗試模仿他，
but I found out that it is very difficult to make good mistakes.
但我發現要犯“好的”錯誤是很難的。
