mathluke · HackerTrans

12 months agodiscuss

You should expect quite a bit of novelty from the IMO, given the constraint of high school level curriculum. The problem setters work very hard to avoid problems that are variations of other contests or solvable by routine methods. That's why this is a very exciting result--you can't just regurgitate homework problem solutions to get a high score at the IMO.

mathluke

12 months agodiscuss

I'd disagree with this take. Math olympiads are some of the most intellectually creative activities I've ever done that fit within a one day time limit. Chess and go don't even come close--I am not a strong player, but I've studied both games for hundreds of hours. (My hot take is that chess is not even very creative at all, that's why classical AI techniques produced super human results many years ago.)

There is no list of tricks that will get a silver much less a gold medal at the IMO. The problem setters try very hard to choose problems that are not just variations of other contests or solvable by routine calculation (indeed some types of problems, like polynomial inequalities, fell out of favor as near-universal techniques made them too routine to well prepared students). Of course there are common themes and patterns that recur--no way around it given the limited curriculum they draw on--but overall I think the IMO does a commendable job at encouraging out-of-the-box thinking within a limited domain. (I've heard a contestant say that IMO prep was memorizing a lot of template solutions, but he was such a genius among geniuses that I think his opinion is irrelevant to the rest of humanity!)

Of course there is always a debate whether competition math reflects skill in research math and other research domains. There's obvious areas of overlap and obvious areas of differences, so it's hard to extrapolate from AI math benchmarks to other domains. But i think it's fair to say the skills needed for the IMO include quite general quantitative reasoning ability, which is very exciting to see LLMs develop.

comments