What will happen if someone doesn’t make it to the IMO team?

Question

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. I want to know whether I will still be able to become a sharp problem solver like the IMO toppers if I regularly practice olympiad problems with full dedication?

Answer 1

Based on this question and your previous question, my impression (correct me if I'm wrong) is that 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).

Answer 2

You have posted two questions on this website so far. Both of them show what is (to me) an unhealthy focus on Olympiad problems.

Firstly I want to remind you that you have value as a living being. Please don't lose sight of that!

Secondly, there are many ways to contribute to mathematics. Some people are really good at solving tricky problems. Some people are really good at noticing when tools from one field might help in another field. Some people are really good at learning a subject deeply, figuring out exactly what makes it tick, and then abstracting away the irrelevant parts to make a more abstract theory which can be applied in greater generality. Some people contribute to math by being really good teachers. Some people contribute to math by becoming rich working for a hedge fund and then donating to mathematical non-profits! These are just a small fraction of the ways people contribute to math.

If you find Olympiad problems to be fun and satisfying, by all means keep solving them. I am sure with practice you can improve. However, if you find yourself feeling sad, overwhelmed, or anxious when you are practicing you should probably just stop. Try to find ways to engage with mathematics which feel good for you.

Please do not make the mistake of thinking that you need to be good at these kinds of problems to make important contributions to mathematics.

Finally, please do not make the mistake of tying your self-worth to your mathematical performance. Think of the people who you love most in your life: probably their mathematical performance is not at the root of why you love them. It is the same for the people who love you. Your worth is unquestionable and is completely independent of your mathematical accomplishment.