A Mathematician Used Claude Fable to Disprove the 87

Key Points:

• Mathematician Levent Alpöge announced a counterexample disproving the long-standing Jacobian conjecture, which posited that a polynomial map with a nonzero constant Jacobian determinant must have a polynomial inverse.
• The counterexample is a concrete three-dimensional polynomial map with a constant Jacobian determinant of -2 that fails to be invertible, as multiple distinct inputs map to the same output, contradicting the conjecture's claim.
• Alpöge credited the result to Anthropic's AI model Fable 5, highlighting the role of advanced AI as a genuine research collaborator capable of producing verifiable mathematical breakthroughs rapidly.
• The claimed disproof, posted publicly with algebra software verification links, awaits formal peer review and verification on arXiv, with the mathematical community cautiously optimistic given the history of previous false proofs.
• This development marks a significant milestone in AI-assisted mathematics, reflecting a growing trend of AI systems autonomously solving open problems and producing formally verified proofs, accelerating mathematical research progress.