openai-imo-2025-proofs

It is possible to take this too far, though - consider the OpenAI IMO proofs[1], for instance, and compare them to Gemini's.[2] [1] https://github.com/aw31/openai-imo-2025-proofs [2] https://arxiv.org/pdf/2507.15855 Appendix A

One point that Karpathy has made in some of his videos is that using additional tokens in the prompt can facilitate computation. If you ask a transformer to do some basic math, it will be more likely to get the right answer (or at least a better approximation) with a more verbose prompt. To me, this backs up the use of more conversational language ("Please," etc.) when prompting. However, that seems to be contradicted by what was shown recently with the successful International Math Olympiad effort. Their prompts, such as https://github.com/aw31/openai-imo-2025-proofs/blob/main/pro... , were very terse. It's hard to tell where the prompt stops and the CoT response starts, in fact. So there is probably some interplay between the need for attention sinks and the use of step-by-step reasoning. It might not be too surprising if the latte

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/

As IMO medalists they would be expected to I'm sure. But this can be verified because the results are public: https://github.com/aw31/openai-imo-2025-proofs/

The proofs were published on GitHub for inspection, along with some details (generated within the time limit, by a system locked before the problems were released, with no external tools). https://github.com/aw31/openai-imo-2025-proofs/tree/main

The solutions were publicly posted to GitHub: https://github.com/aw31/openai-imo-2025-proofs/tree/main

> it’s also more efficient [than o1 or o3] with its thinking. "So under his saturate response, he never loses. For her to win, must make him unable at some even -> would need Q_{even-1}>even, i.e. some a_j> sqrt2. but we just showed always a_j<=c< sqrt2. So she can never cause his loss. So against this fixed response of his, she never wins (outcomes: may be infinite or she may lose by sum if she picks badly; but no win). So she does NOT have winning strategy at λ=c. So at equality, neither player has winning strategy."[1] Why use lot word when few word do trick? 1. https://github.com/aw31/openai-imo-2025-proofs/blob/main/pro...

Interesting that the proofs seem to use a limited vocabulary: https://github.com/aw31/openai-imo-2025-proofs/blob/main/pro... Why waste time say lot word when few word do trick :) Also worth pointing out that Alex Wei is himself a gold medalist at IOI.