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AlphaProof's Greatest Hits
Here I’ll try to explain the coolest ideas in each of AlphaProof’s IMO 2024 solutions. AlphaProof produces proofs in Lean, and each Lean proof is composed of a series of tactics. So I’ll pick out the tactics that correspond to these ideas in the proofs for problems 1, 2 and 6 (the three problems that AlphaProof solved). AlphaProof has developed its own proving style, so figuring out what it’s doing can involve some detective work.
The full AlphaProof solutions, annotated by , are available here- I will only include snippets of the proofs in this post. Reminder that the way AlphaProof solves these problems is by proposing many solution candidates, attempting to prove and disprove each of them, and then eventually finding a proof only for the correct answer. Finding these mathematical ideas is hard enough, and having to prove them in Lean makes things even harder.
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