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Comment by Davidzheng | Hacker News Reader

No I assure you >50% of working mathematicians will not score gold level at IMO consistently (I'm in the field). As the original parent said, pretty much only ppl who had the training in high school can. Like number theorists without training might be able to do some number theory IMO questions but this level is basically impossible without specialized training (with maybe a few exceptions of very strong mathematicians)

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> No I assure you >50% of working mathematicians will not score gold level at IMO consistently (I'm in the field)

I agree with you. However, would a lot of working mathematicians score gold level without the IMO time constraints? Working mathematicians generally are not trying to solve a problem in the time span of one hour. I would argue that most working mathematicians, if given an arbitrary IMO problem and allowed to work on it for a week, would solve it. As for "gold level", with IMO problems you either solve one or you don't.

You could counter that it is meaningless to remove the time constraints. But we are comparing humans with OpenAI here. It is very likely OpenAI solved the IMO problems in a matter of minutes, maybe even seconds. When we talk about a chatbot achieving human-level performance, it's understood that the time is not a constraint on the human side. We are only concerned with the quality of the human output. For example: can OpenAI write a novel at the level of Jane Austen? Maybe it can, maybe it can't (for now) but Jane Austen was spending years to write such a novel, while our expectation is for OpenAI to do it at the speed of multiple words per second.

I mean. Back when I was practicing these problems sometimes I would try them on/off for a week and would be able to do some 3&6's (usually I can do 1&4 somewhat consistently and usually none of others). As a working mathematician today, I would almost certain not be able to get gold medal performance in a week but for a given problem I guess I would have ~50% chance at least of solving it in a week? But I haven't tried in a while. But I suspect the professionals here do worse at these competition questions than you think. I mean certain these problems are "easy" compared to many of the questions we think about, but expertise drastically shifts the speed/difficulty of questions we can solve within our domains, if that makes sense.

Addendum: Actually I am not sure the probability of solving it in a week is not much better than 6 hours for these questions because they are kind of random questions. But I agree with some parts of your post tbf.

> It is very likely OpenAI solved the IMO problems in a matter of minutes, maybe even seconds

Really? My expectation would have been the opposite, that time was a constraint for the AIs. OpenAI's highest end public reasoning models are slow, and there's only so much that you can do by parallelization.

Understanding how they dealt with time actually seems like the most important thing to put these results into context, and they said nothing about it. Like, I'd hope they gave the same total time allocation for a whole problem set as the human competitors. But how did they split that time? Did they work on multiple problems in parallel?

I sense we may just have a different experience related to colleagues skill sets as I can think of 5 people I could send some questions too and I know they would do them just fine. Infact we often have done similar problems on a free afternoon and I often do similar on flights as a way to pass the time and improve my focus (my issue isn't my talent/understanding at maths, it's my ability to concentrate). I don't disagree that some level of training is needed but these questions aren't unique, nor impossible, especially as said training does exist and LLM's can access said examples. LLM's also have brute force which is a significant help with these type of issues. One particular point is that Math of all the STEM topics to try and focus on probably is the best documented alongside CS.

I mean these problems you can get better with practice. But if you haven't solved many before and can do them after an afternoon of thought I would be very impressed. Not that I don't believe you, it's just in my experience people like this are very rare. (Also I assume they have to have some degree of familarity of some common tricks otherwise they would have to derive basic number theory from scratch etc and that seems a bit much for me to believe)

I think honestly it's probably different experiences and skillsets. I find these sort of things doable bar dumb mistakes by myself, yet there will be other things I'll get stressed and not be able to do for ages (some lab skills no matter the number of times I do them and some physical equation derivations that I regularly muck up). I maybe sometimes assume that what comes easy for me, comes easy for all, and what I struggle with, everyone struggles with and that's probably not always the case. Likewise I did similar tasks as a teen in school and assume that is possibly the case for many academically bright so to speak but perhaps isn't so that probably helped me learn some tricks that I may not have otherwise. But as you say I do feel that you can learn the tricks and learn how to do them, even in older age (academically speaking) if you have the time and the patience and the right guide.

Here you go — you did this type of problems as a kid/teenager. 1) you likely have a talent for it 2) you have some training.

I did participate in math/informatics olympiads as a teenager and even taught it a little and from my experience, some type of people just _like_ that sort of problems naturally, they tickle their minds, and given time this people would develop to insane levels at it.

'Normal people', in my experience, even in math departments, don't like that type of problems, and would not fare well with them.

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