Thurston's answer is obviously well meaning and trying to breath inspiration into people who are pursuing maths as a discipline, but it should be observed anyone taking him at his word without context will be led astray. It isn't useful guidance for a young aspiring mathematician because it is generic, contains nothing actionable and not even a clue on how to judge a successful/failed state as they move through life.

Even "your name will go down in history if you consistently find patterns in daily life that other people can't see" would probably be more useful advice to the next Euler or Gauss.

> The product of mathematics is clarity and understanding.

Mathematics is clarity and understanding of mathematical objects which is a very small subset of the things that most people seek when they go looking for clarity and understanding. Anyone looking for clarity and understanding in the abstract is better off starting their search in the Psychology or possibly the Philosophy departments.

I don't think he was being arrogant with that quote, but I do think that it is the perspective of someone who has spent so much time looking at maths they might have lost track of all the social manoeuvring that is what satisfies most humans. In my case I'd rather have a deep understanding of what someone is saying to me than of Fermat's Last Theorem - communication abilities tends to be more of a bottleneck to satisfaction than abstraction abilities. Even in Thurston's answer, he is alluding to the fact that communicating with other mathematicians is as important to him as understanding abstract concepts.

> follow your heart and your passion. Bare reason is likely to lead you astray

This is lousy advice. Following your passions only works for people lucky enough to have productive passions. A lot of people are passionate about eating good food - if they want to be productive they will need a plan other than following their passions.