Life is too short to be living someone else's dream.

数学的本质在于它的自由。

当没有人相信你的时候，你必须相信自己。

The freedom then of man, and liberty of acting according to his own will, is grounded on his having reason, which is able to instruct him in that law he is to govern himself by, and make him know how far he is left to the freedom of his own will.

I don't have any particular recipe [for developing new proofs] ... It is the reason why doing research is challenging as well as attractive. It's like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out.

有时候要大胆，有时候要小心，一个聪明人知道什么时候该怎么做。