Andrew Wiles is the Cambridge mathematician who gained international recognition for solving Fermat’s Last Theorem, a proof that took him seven years but which, until he solved it, had remained unsolved for 356. Years ago I saw an interview with him, which I sadly have never found again, in which he described what it was like to see the light after devoting every free moment to the proof for those seven years. He started to cry and then, being a very proper English academic, apologized for crying.
Here is what he said about doing mathematics at a high level: “What you have to handle is … accepting the state of being stuck … it’s part of the process, and you have to accept, you have to learn to enjoy that process. Yes, you don’t understand, but you have faith that you will understand and that you have to go through this. It’s like anything. It’s like training in sport. You want to run fast, you have to train.”
That willingness to stay with something even when you are stuck takes an awful lot of curiosity, if you ask me!
That quotation is from a presentation he made at the Heidelberg Laureate Forum: https://www.youtube.com/watch?v=KaVytLupxmo&feature=youtu.be