The arithmetic of modular forms is a key to understanding the deeper structures of number theory.
界限定义了我们的身份。它们定义了什么是“我”,什么不是“我”。界限显示了我结束的地方和他人开始的地方,引导我拥有一种所有权感。
我没有任何特别的秘诀(用于开发新的证明)……这就是为什么做研究既具有挑战性又具有吸引力的原因。这就像在丛林中迷路,试图利用你能收集到的所有知识来想出一些新的技巧,并且如果运气好的话,你可能会找到出路。
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.
语言中最具破坏性的短语是:“一直都是这样做的。”