Cross-posted from here.
I am highly interested in mathematics, and solving Olympiad maths problems has been a type of hobby for me. But due to my age, I will never be able to give the Olympiads a go again. Will I always be behind the toppers, career-wise? Can I ever catch up to them?
It sounds like you are driven to become a hardcore problem-solver, and you’ve had fun participating in Math Olympiad, which you view as the pinnacle of problem-solving – but you didn’t end up topping Olympiad, you’re now too old to compete, you’re disappointed that you can’t try again, and you’re maybe a bit regretful in feeling that you could have practiced with fuller dedication.
Well, I have good news for you! This may feel a bit hopeless at the moment, but it’s actually the opposite. And when I say that, I’m not just talking about opportunities to mentally reframe the situation to help cope with the pain (such as loosening psychological ties between problem-solving ability and self-worth, which would also be healthy but is not the subject of this answer). I mean that, in an absolute sense, you can still become an amazing problem-solver and get recognized for it. This is just the beginning.
First of all, if you’re at university, then there might be even higher competition math that you are eligible for – for instance, in the USA/Canada, any undergraduate can take the Putnam Exam, the topping of which is (in my experience) generally considered even more impressive than topping any high school Math Olympiad (even International Math Olympiad).
But second, and more importantly, math competitions like Olympiad and Putnam are not the pinnacle of problem-solving. It just seems that way because in school, that’s what lots of “math”-y people focus on and get recognized for, so it’s always in your face. But think about it – of all the world’s famous problem-solvers, how many of them gained their reputation from topping math competitions? None of them. Even amongst the minority that did top math competitions, that’s not what they’re known for. They’re generally known for their problem-solving success on more widely branching paths that they pursued after their initial schooling. Below are some of the most well-known of these paths, along with links to further reading about some of their “toppers”:
- Research in math and associated disciplines. "Toppers" of this path include Fields Medalists, Abel Prize Winners, and awardees of other highest honors.
- Application of math to solve hard practical problems in industry. I don't know of any coordinated awards for this kind of thing (besides becoming very wealthy!) but some individual "toppers" of this path include Jeff Dean, Jim Simons, Demis Hassabis, and pretty much any "math"-y person who was a founder or early employee of a company that has become widely known (especially in tech / engineering / finance).