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Jacobian Conjecture

All articles tagged with #jacobian conjecture

science1 month ago•4 min saved

AI-Generated Tiny 3D Formula Upends Century-Old Jacobian Conjecture

A three-dimensional polynomial with a constant Jacobian determinant (-2) serves as a counterexample to the Jacobian conjecture in dimensions greater than two, while the two-dimensional case remains open. Discovered by Levent Alpöge using Anthropic’s Claude Fable 5, the remarkably simple formula is easy to verify and highlights AI’s potential to uncover surprising mathematical objects, signaling a new avenue for AI-assisted breakthroughs in mathematics.

via SciTechDaily|

#ai #algebraic-geometry #counterexample

technology1 month ago•5 min saved

AI tool Fable 5 allegedly disproves the Jacobian conjecture

A mathematician, Levent Alpöge, used Anthropic’s Fable 5 to claim a counterexample to the Jacobian conjecture, a nearly 90-year open problem in algebraic geometry. Experts warn that a single counterexample, while notable, is not equivalent to a full proof and may offer limited insight, though the episode underscores AI’s potential in assisting mathematical research and discovery, with discussions also touching on OpenAI’s related progress.

via Mashable|

#academia #artificial-intelligence #fable-5

science1 month ago•4 min saved

AI-Engine Counterexample Cracks Century-Old Jacobian Conjecture

Mathematician Levent Alpöge used Anthropic’s Claude Fable 5 to forge a concrete three-variable polynomial with Jacobian determinant -2 that is not invertible, producing a verifiable counterexample to the Jacobian conjecture (pending arXiv peer review); the episode underscores AI as a genuine research collaborator and highlights the rise of formal verification like Lean in AI-driven mathematics.

via Glitchwire|

#ai-math #anthropic #arxiv