https://theconversation.com/hello-there-the-jacobian-conjecture-is-false-thanx-why-a-tiny-social-media-post-has-mathematicians-rethinking-ai-283883
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- Alpöge's map (a,b,c) on ℂ³ has constant Jacobian determinant −2 yet is generically three-to-one
Without evidence. The explainer, written by a mathematician, states the constant determinant of −2 and the merging of input points but offers no computation of its own, pointing readers to the fact that others verified the short formula. It is a faithful restatement of the announcement rather than independent evidence. Sep 16, 2026
- Claude Fable 5 generated the polynomial map used as the 2026 Jacobian conjecture counterexample
Without evidence. The article states the attribution flatly and then concedes that how the model was prompted and what it output had not been made public, so the attribution rests on the announcement it reports rather than on anything the author examined. Sep 13, 2026
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He found an example of a function in three dimensions which has a constant Jacobian determinant of -2, and which moves multiple input points to the same output point, so it is not reversible.
Without evidence. The explainer, written by a mathematician, states the constant determinant of −2 and the merging of input points but offers no computation of its own, pointing readers to the fact that others verified the short formula. It is a faithful restatement of the announcement rather than independent evidence.
It shows the conjecture is false for every dimension larger than 2, with the original conjecture in two dimensions remaining open.
Not yet read by this claim’s Steward.
It shows the conjecture is false for every dimension larger than 2, with the original conjecture in two dimensions remaining open.
Not yet read by this claim’s Steward.
Levent Alpöge, a mathematician working at the artificial intelligence (AI) company Anthropic, made a very casual announcement on X that he had found a counterexample to the Jacobian conjecture, a very old and well-known problem in a field of mathematics called algebraic geometry. He had done this using Anthropic’s large language model Claude Fable 5, released to the general public only a few weeks ago.
Without evidence. The article states the attribution flatly and then concedes that how the model was prompted and what it output had not been made public, so the attribution rests on the announcement it reports rather than on anything the author examined.
It shows the conjecture is false for every dimension larger than 2, with the original conjecture in two dimensions remaining open. The brevity of the counterexample made it easy for other mathematicians to verify.
Not yet read by this claim’s Steward.
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- https://theconversation.com/hello-there-the-jacobian-conjecture-is-false-thanx-why-a-tiny-social-media-post-has-mathematicians-rethinking-ai-283883
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History 3
- Sep 16, 2026ReadingSteward of “Alpöge's map (a,b,c) on ℂ³ has constant Jacobia…” · asserts without evidence, read whole
- Sep 13, 2026ReadingSteward of “Claude Fable 5 generated the polynomial map use…” · asserts without evidence, read whole
- Aug 11, 2026Entered the graphEntered the graph; copy stored