141–150 of 254 posts
I think we are having a Deep Blue vs. Kasparov moment in Competitive Math right now. This is a large progress from just a few years ago and yet I think we still are really far away from even a semi-respectable AI mathematician. What an exciting time to be alive!
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Childish. And, of course they must have known there was an official LLM cohort taking the real test, and they probably even knew that Gemini got a gold medal, and may have even known that Google planned a press release for today.
I think maybe all Altman companies have used tactics like this. > We were trying to get a big client for weeks, and they said no and went with a competitor. The competitor already had a terms sheet from the company were we trying to sign up. It was real serious. > We were devastated, but we decided to fly down and sit in their lobby until they would meet with us. So they finally let us talk to them after most of the…
Most critical piece of information I couldn’t find is - how many shot was this? Could it understand the solution is correct by itself (one-shot)? Or did it have just great math intuition and knowledge? How the solutions were validated if it was 10-100 shot?
Do I understand it correctly that OpenAI self-proclaimed that they got their gold, without the official IMO judges grading their solutions?
Well, I don't doubt that they did get those results, but it is clear now that it was not an official collaboration. It was heavily implied in a statement by IMO's president a few days ago (the one where they said they'd prefer AI companies wait a week before announcing, so that the focus is first on the human competitors). Goog had an official colab with IMO, and we can be sure they got those results under the impose…
Besides, they still specialized Gemini for the IMO in other ways:
> we additionally trained this version of Gemini on novel reinforcement learning techniques that can leverage more multi-step reasoning, problem-solving and theorem-proving data. We also provided Gemini with access to a curated corpus of high-quality solutions to mathematics problems, and added some general hints and tips on how to approach IMO problems to its instructions.
This is making mathematics too systematic and mechanical, and it kills the joy of it....
This year, our advanced Gemini model operated end-to-end in natural language, producing rigorous mathematical proofs directly from the official problem descriptions I think I have a minority opinion here, but I’m a bit disappointed they seem to be moving away from formal techniques. I think if you ever want to truly “automate” math or do it at machine scale, e.g. creating proofs that would amount to thousands of page…
I'm actually prepared to agree wholeheartedly with what you say here: I don't think there'd be any realistic way to produce thousand-page proofs without formalization, and certainly I wouldn't trust such a proof without some way to verify it formally. But I also don't think we really want them all that much!
The ultimate reason I think is that what really lights a fire under most mathematicians is the desire to know why a result is true; the explanation is really the product, much more so than just the yes-or-no answer. For example, I was never a number theorist, but I think most people who are informed enough to have an opinion think that the Riemann Hypothesis is probably true, and I know that they're not actually waiting around to find out. There are lots of papers that get published whose results take the form "If the Riemann Hypothesis is true then [my new theorem]."
The reason they'd still be excited by a proof is the hope, informed by experience with proofs of earlier long-standing open problems, that the proof would involve some exciting new method or perspective that would give us a deeper understanding of number theory. A proof in a formal language that Lean says is true but which no human being has any hope of getting anything from doesn't accomplish that.
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I found the proofs you were referring to: Google https://storage.googleapis.com/deepmind-media/gemini/IMO_202... OpenAI https://github.com/aw31/openai-imo-2025-proofs/
Gemini is clearer but MY GOD is it verbose. e.g. look at problem 1, section 2. Analysis of the Core Problem - there's nothing at all deep here, but it seems the model wants to spell out every single tiny logical step. I wonder if this is a stylistic choice or something that actually helps the model get to the end.
I think we are having a Deep Blue vs. Kasparov moment in Competitive Math right now. This is a large progress from just a few years ago and yet I think we still are really far away from even a semi-respectable AI mathematician. What an exciting time to be alive!
Terrence Tao, in a recent podcast, said that he's very interested in "working along side these tools". He sees the best use in the near future as "explorers of human set vision" in a way. (i.e. set some ideas/parameters and let the LLMs explore and do parallel search / proof / etc) Your comparison with chess engines is pretty spot-on, that's how the best of the best chess players do prep nowadays. Gone are the multi…