Astounding in what sense? I assume you are aware of the standard of Olympiad problems and that they are not particularly high. They are just challenging for the age range, but they shouldn't be for AI considering they aren't really anything but proofs and basic structured math problems.
Considering OpenAI can't currently analyse and provide real paper sources to cutting edge scientific issues, I wouldn't trust it to do actual research outside of generating matplotlib code.
I did competitive math in high school and I can confidently say that they are anything but "basic". I definitely can't solve them now (as an adult) and it's likely I never will. The same is true for most people, including people who actually pursued math in college (I didn't). I'm not going to be the next guy who unknowingly challenges a Putnam winner to do these but I will just say that it is unlikely that someone who actually understands the difficulty of these problems would say that they are not hard.
For those following along but without math specific experience: consider whether your average CS professor could solve a top competitive programming question. Not Leetcode hard, Codeforces hard.
Thanks for speaking sense. I think 99% of people saying IMO problems are not hard would not be able to solve basic district-level competition problems and are just not equipped to judge the problems.
And 1% here are those IMO/IOI winners who think everyone is just like them. I grew up with them and to you, my friends, I say: this is the reason why AI would not take over the world (and might even not be that useful for real world tasks), even if it wins every damn contest out there.
I feel like people see the question (or even the solution), they can actually understand what it says because it’s only using basic algebraic notation, then assume it must be easy to solve. Obviously it must be easier than that funny math with weird symbols…
> I assume you are aware of the standard of Olympiad problems and that they are not particularly high.
Every time an LLM reaches a new benchmark there’s a scramble to downplay it and move the goalposts for what should be considered impressive.
The International Math Olympiad was used by many people as an example of something that would be too difficult for LLMs. It has been a topic of discussion for some time. The fact that an LLM has achieved this level of performance is very impressive.
You’re downplaying the difficulty of these problems. It’s called international because the best in the entire world are challenged by it.
you meaning specific IMO training or general math training? Latter is certainly needed, former being needed in my opinion is a general observation for example about the people who make it on the teams.
I feel like I've noticed you you making the same comment 12 places in this thread -- incorrectly misrepresenting the difficulty of this tournament and ultimately it comes across as a bitter ex.
Here's an example problem 5:
Let a1,a2,…,an be distinct positive integers and let
M=max1≤i<j≤n.
Find the maximum number of pairs (i,j) with 1≤i<j≤n for which (ai +aj )(aj −ai )=M.
I asked chatGPT. However it's saying that's 2022 problem 5, however that seems to be clearly wrong... Moreover I can't find that problem anywhere so I don't know if it's a hallucination or something from it's training set that isn't on the internet....
IMO questions and Andrew Wiles solving Fermat's last theorem are two vastly different things. One is far harder than the other and the effort he put in and thinking needed is something very few can do. He also did some other fascinating work that I couldn't hope to understand fully. There is a gulf between FLT and IMO types of proofs.
Considering OpenAI can't currently analyse and provide real paper sources to cutting edge scientific issues, I wouldn't trust it to do actual research outside of generating matplotlib code.