Human mathematicians are being outcounterexampled

6 days ago

ChatGPT disproved Erdős’ Unit Distance conjecture; human mathematicians validated it, but initially, it wasn't formalized in Lean.
Logical Intelligence autoformalized the counterexample in Lean, and Boris Alexeev achieved a full Lean formalization using OpenAI's Sol model, generating 1.2 million lines of Lean code in three weeks.
During a workshop, an AI-generated exposition on finite flat group schemes contained a false claim; AI identified and provided a counterexample to it.
AI, via Sol and Fable, found a counterexample to Grothendieck's question on group schemes of order n. Akhil Mathew formalized it in Lean, and it was added to mathlib.
AI tools like Sol and Fable enabled rapid progress in formalizing mathematical projects, such as modularity lifting theorems, and are becoming essential for researchers.
Fable found a counterexample to the Jacobian Conjecture, a long-standing open problem. Paul Lezeau formalized it, and DeepMind's repository facilitated verification.
AI-generated mathematics requires formal verification for trust, but understanding the insights from counterexamples remains a key challenge for human mathematicians.

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