Earlier quoted context omitted.
Very few humans go after this type of the training. In my "math talent" school (most of the Serbian/Yugoslavian medal winners came from it), at most a dozen students "trained" for this over 4 high school generations (500 students). Problems are certainly not trivial, but humans are not really putting all their effort into it either, and the few that do train for it, on average medal 50% of the time and get a silver o…
This is disingenuous. People who train are already self selected people who are talented in math. And in the people who train not everyone gets to this level. Sadly i speak from personal experience.
Most students were simply not interested. And certainly, not everybody is equally talented, but the motivation to achieve competition success is needed too — perhaps you had the latter but not enough of the former. I also believe competitive maths is entirely different from research maths (time pressure, even luck is involved for a good idea to come up quickly, etc). Since you said you were a potential bronze medal winner, it might not even be a talent issue but maybe you just had great competition and someone had the better luck in one or two tests to rank above you (better luck as in the right idea/approach came to them quicker, or the type of problem that appeared on the test suited them more). And if you are from a large country like USA, China or Russia (topping the medal table), it's going to be freaking hard to get into a team since you'll have so many worthy students (and the fact they are not always scoring only golds for their teams out of such large pools tells me that the performance is not deterministic).
As a mathematician, I am sure you'd agree you'd want to run a lot more than a dozen tests to establish statistical significance for any ranking between two people at competitive maths IMO style, esp if they are close in the first few. As an anecdote, many at my school participated in national level maths and informatics competitions (they start at school level, go on to county/city level to nation level) — other than the few "trained" competitors staying at the top, the rest of the group mostly rotated in the other spots below them regardless of the level (school/county/nation). We've actually joked amongst ourselves about who had the better intuition "this time around" for a problem or two, while still beating the rest of the country handily (we've obviously had better base level of education + decently high base talent), but not coming close to "competitors".
I, for instance, never enjoyed working through math problems and math competitions (after winning a couple of early age local ones): I've finished the equivalent of math + CS MSc while skipping classes by only learning theory (reading through axioms, theorems and proofs that seemed non-obvious) and using that to solve problems in exams. I've mostly enjoyed building things with the acquired knowledge (including my own proofs on the spot, but mostly programming), even though I understood that you build up speed with more practice (I was also lazy :)).
So, let's not trivialize solving IMO-style problems, but let's not put them on a pedestal either. Out of a very small pool of people who train for it, many score higher than AI did here, and they don't predict future theoretical math performance either. Competition performance mostly predicts competition performance, but even that with large error bars.