As a person from a similar background (IMO medalist, etc.) who has considered similar criteria, one field I have been thinking a lot about is formal verification. It's mathematically challenging in that it can involve a lot of complicated, unintuitive mathematical logic, and it's verifiable in that you can know when the proof checker succeeds that you got things "right", although I don't think there are rewards like in trading or ML competitions, nor is it competitive in the way you describe. (Personally, I now think this last point is a good thing—I loved the math but hated the zero-sum nature of math competitions. But, if this counts for anything, I think there are people trying to build an AI to "win an IMO gold medal" with formal proofs.)

I am not very confident about the impact of such a career, but I think there's at least a decent chance of high impact. 80000 Hours has a short review with some reasons to believe in its potential and some cases for being bearish, although the latter cases focus on AI safety applications and I think applications to cybersecurity are more direct and also have solid potential for impact. Also, I suspect that a formal verification career that's optimized for impact will look completely different from one that's optimized to be mathematically challenging. But I would guess that, at the very least, the path to high impact is more plausible than derivatives trading or finance.

As a person from a similar background (IMO medalist, etc.) who has considered similar criteria, one field I have been thinking a lot about is formal verification. It's mathematically challenging in that it can involve a lot of complicated, unintuitive mathematical logic, and it's verifiable in that you can know when the proof checker succeeds that you got things "right", although I don't think there are rewards like in trading or ML competitions, nor is it competitive in the way you describe. (Personally, I now think this last point is a good thing—I loved the math but hated the zero-sum nature of math competitions. But, if this counts for anything, I think there are people trying to build an AI to "win an IMO gold medal" with formal proofs.)

I am not very confident about the impact of such a career, but I think there's at least a decent chance of high impact. 80000 Hours has a short review with some reasons to believe in its potential and some cases for being bearish, although the latter cases focus on AI safety applications and I think applications to cybersecurity are more direct and also have solid potential for impact. Also, I suspect that a formal verification career that's optimized for impact will look completely different from one that's optimized to be mathematically challenging. But I would guess that, at the very least, the path to high impact is more plausible than derivatives trading or finance.