AI-Assisted Mathematical Problem Solving: Collaborative Workflow on Erdős Problem #367
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dwohnitmok
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Summary
Mathematician Terence Tao describes a collaborative mathematical problem-solving process involving AI tools. The article details how mathematician Wouter van Doorn proposed a disproof of Erdős problem #367, Terence Tao used Google's Gemini Deepthink AI to verify a key identity, then Boris Alexeev used Aristotle AI tool to formalize the proof in Lean. The process demonstrates how AI is becoming integrated into mathematical research workflows, with humans and AI collaborating to solve complex problems.
Key quotes
· 5 pulledOver at the Erdos problem website, AI assistance is now becoming routine.
I posed this problem to Gemini Deepthink, which (after about ten minutes) produced a complete proof of the identity (and confirmed the entire argument).
I then spent about half an hour converting the proof by hand into a more elementary proof, which I presented on the site.
Boris Alexeev used the Aristotle tool from Harmonic to complete the Lean formalization, making sure to formalize the final statement by hand to guard against AI exploits.
This process took two to three hours, and the output can be found at https://borisalexeev.com/t/Erdos367.lean
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