Comment by bluecalm
5 days ago
Imo competitive math (or programming) is about knowing some tricks and then trying to find a combination of them that works for a given task. The number of tricks and depth required is much less than in go or chess.
I don't think it's very creative endeavor in comparison to chess/go. The searching required is less as well. There is a challenge processing natural language and producing solutions in it though.
Creativity required is not even a small fraction of what is required for scientific breakthroughs. After all no task that you can solve in 30 minutes or so can possibly require that much creativity - just knowledge and a fast mind - things computers are amazing at.
I am AI enthusiast. I just think a lot of things that were done so far are more impressive than being good at competitive math. It's a nice result blown out of proportion by OpenAI employees.
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.
What you are missing about chess and go is that those games are not about finding one true solution. They are very psychological games (at human level) and are about finding moves that are difficult to handle for the opponent. You try to understand how your opponent thinks and what is going to be unpleasant for them. This gives a lot of scope for creative and psychological warfare.
In competitive math (or programming) there is one correct solution and no opponent. It's just not possible for it to be very creative endeavor if those solutions can be found in very limited time.
>>(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!)
So you have not only chosen to ignore the view of someone who is very good at it but also assumed that even though the best preparation for them is to memorize a lot of solutions it must be about creativity for people who are not geniuses like this guy? How does it make sense at all?
> They are very psychological games (at human level) and are about finding moves that are difficult to handle for the opponent. You try to understand how your opponent thinks and what is going to be unpleasant for them. This gives a lot of scope for creative and psychological warfare.
And yet even basic models which can run on my phone win this psychological warfare with best players in the world. The scope of problems on IMO is unlimited. Please note that IMO is won by literally best high-school students in the world and most of them are unable to solve all problems (even gold medal winners). Do you think that they are dumb and unable to learn "few tricks"?
>In competitive math (or programming) there is one correct solution and no opponent. It's just not possible for it to be very creative endeavor if those solutions can be found in very limited time.
That's absurd. You could say same things about math research (and "one correct solution" would be wrong as it is for IMO), do you consider it something that's not creative?
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