In this post, the author delves into AlphaProof’s solutions for problems 1, 2, and 6 from IMO 2024. AlphaProof’s proving style involves proposing and testing multiple solutions before finding the correct one. Problem 1 involves determining that the set of even integers is the answer, and the proof involves intricate steps. Problem 2 concludes that the only solution is $(1, 1)$ by considering the number $ab + 1. The solution for Problem 6 is to find that there are at most 2 distinct rational numbers in the form $f(r) + f(-r)$, achieved by clever constructions. The author expresses amazement at the ability of AlphaProof to generate such complex proofs.
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