Comment by bwfan123

This paper [1] shows that gemini pro 2.5 without data-contamination and some minimal prompting (llm orchestration) can solve problems 1-5 on imo 2025.

[1] https://arxiv.org/pdf/2507.15855

For problems with 2 page solutions, the search space of solutions is likely limited, and hence could be brute-forced by a search. Combinatorics is likely the hold-out since there are no set approaches one could take ie training data wont cover the space of techniques - which could explain why problem 6 stumped the llms.

Also, in the future the minimal diligence IMO problem setters could do is to test against these LLMs to ensure that they cant solve them. Further, one could expect these tools to become available to contestents just like calculators are allowed in tests these days.

Still, it is impressive for the LLMs to be able to craft watertight arguments in math at the IMO level without the use of provers.