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...
Together, Taniyama and Shimura worked on the complex mathematics of modular functions. 谷山丰和志村五郎一起进行模函数方面复杂数学的研究 I really can't explain what a modular function is in one sentence. 我实在不能用一句话...
It looks so simple yet the complexity, especially arithmetic complexity, is immense. 它看来如此简单，然而其复杂性，尤其是几何复杂性，极大。 Every point on the doughnut is the solution to an equation. 甜甜圈上的每个点都...
In the 70s Fermat was no longer in fashion. 70年代时，费马不再热门 At the same time Andrew Wiles was just beginning his career as a mathematician. 与此同时，安德鲁怀尔斯正开始其作为数学家的生涯。 He went to Cambridge...
Well how many numbers are there to beat that with? 要这么做的话得要试多少个数? You've got to do it for infinitely many numbers. 你得要这么试上无穷无尽的数字 So after you've done it for one, how much closer have you got? 那么...
Fermat made lots of marginal notes. 费马写了相当多的页栏笔记 People took them as challenges and over the centuries every single one of them has been disposed of, 人们将那些视为挑战，数世纪以来，其中的每一条都已被解...
X squared plus y squared equals zee squared, and you can ask: x+y=z，你可以问： well what are the whole numbers solutions of this equation? 那么这个等式的整数解是什么? And you quickly find there's a solution 3 squared plus 4 square...
Pierre de Fermat was a 17th-century French mathematician who made some of the greatest breakthroughs in the history of numbers. 皮埃尔德费马是17世纪时期的法国数学家，他在数学历史上成就了一些最伟大的突破。 His insp...
This is the story of one man's obsession with the world's greatest mathematical problem. 这个故事是关于一个人对于世界上最大数学难题的沉迷 For seven years Professor ANDREW WILES worked in complete secrecy, creating the calculat...
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. 或许描述我研究数学的经历最恰当的比方，就是进入一个黑暗的大宅中 Because, when one goes into the first room and it's da...
