I don't have any post graduate education. I'm ok at math, but not exceptional. I managed to publish a paper a few years ago that is mostly a math paper that I'm really proud of. <a href="https://arxiv.org/abs/1809.04052" rel="nofollow">https://arxiv.org/abs/1809.04052</a> (It's a useful algorithm for big-data work, but it's also a bit of math about how to align probability distributions so they collide as much as possible. I tell my kids that daddy discovered something new about how triangles fit together.)<p>There are lots of useful corners of math out there, lots of things that are worth thinking about that no one has thought about just because there are so many things to think. There are plenty of things worth poking at that aren't The Big Problems.
Here's a longer article by Thurston on the same ideas <a href="https://arxiv.org/abs/math/9404236" rel="nofollow">https://arxiv.org/abs/math/9404236</a>. Highly recommend irrespective of how involved you are with mathematics.
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.<p>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.<p>> The product of mathematics is clarity and understanding.<p>Mathematics is clarity and understanding of <i>mathematical objects</i> 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.<p>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.<p>> follow your heart and your passion. Bare reason is likely to lead you astray<p>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.
RIP Bill Thurston! Thank you for sharing!<p>His mini-essay made a lot of sense. I think he nailed it in the beginning by saying that the world collectively benefits from Mathematics as a whole. Or rather, benefits are a "side effect" of people's Mathematical achievements.
I like the Feynman quote in the comments: "You keep on learning and learning, and pretty soon you learn something no one has learned before."
That's beautiful -- thank you for sharing the post. I don't get to think about pure math very often any more, but this was a wonderful reminder of clarity in a world that's a little more disordered than usual.<p>One of the little joys of math, well known, but always makes me smile: Though there are infinitely many rational numbers, they are countable.
Russell once wrote "Work is of two kinds: first, altering the position of matter at or near the earth's surface relatively to other such matter; second, telling other people to do so." Maths is a constructive proof that his case analysis was not exhaustive.
"This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help "<p>Yeah, that's StackOverflow for ya (or MathOverflow I guess).