--- title: Claude 'Fable 5' just disproved an 87-year-old math... description: An AI model called 'Claude Fable 5' reportedly produced a counterexample to the Jacobian conjecture, an open mathematical problem since 1939. The... canonical: https://daily.dev/posts/claude-fable-5-just-disproved-an-87-year-old-math-conjecture-by-prompting-uhggmvehq copyright: © 2026 Daily Dev Ltd. terms: https://daily.dev/tos/ twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Claude 'Fable 5' just disproved an 87-year-old math conjecture by prompting | daily.dev og:description: An AI model called 'Claude Fable 5' reportedly produced a counterexample to the Jacobian conjecture, an open mathematical problem since 1939. The... og:url: https://daily.dev/posts/claude-fable-5-just-disproved-an-87-year-old-math-conjecture-by-prompting-uhggmvehq og:image: https://api.daily.dev/og/posts/UhggmVehq.png og:image:alt: Claude 'Fable 5' just disproved an 87-year-old math conjecture by prompting og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Claude 'Fable 5' just disproved an 87-year-old math conjecture by prompting **[Trends](https://daily.dev/sources/trends)** · 3 min read · 3 upvotes · 0 comments ## Summary An AI model called 'Claude Fable 5' reportedly produced a counterexample to the Jacobian conjecture, an open mathematical problem since 1939. The counterexample is a concrete 3D polynomial function where three distinct inputs map to the same output, violating the conjecture's invertibility requirement. The math community still needs to independently verify the result. The find highlights AI's structural advantage in counterexample-finding tasks: large search spaces with clear verification criteria. It also raises broader questions about how many other long-standing open problems could fall to AI-assisted search, and whether access restrictions on frontier models are limiting wider scientific progress. ## Content An 87-year-old math conjecture is dead, and the discourse is split between "this changes everything" and "a machine found a needle in a haystack, calm down." The setup: the Jacobian conjecture, posed in 1939, claimed that any polynomial map with a constant nonzero Jacobian determinant must be globally invertible. Anthropic mathematician Levent Alpöge, working with Claude Fable 5 during the World Cup final, found a counterexample — a cubic polynomial map from ℂ³ to itself that sends three distinct input points to the same output. Jacobian determinant is a constant −2 everywhere. Not invertible. Conjecture dead. The proof verified in Lean within hours, and Terence Tao wrote up a clean exposition shortly after. The part that's making people's heads spin: mathematicians had estimated any counterexample would need polynomials of degree up to 200. Fable found one at degree 7. The prompts Alpöge used were reportedly something like "do a breakthrough" and "enough, do it." That detail is doing a lot of work in the discourse right now. Fields medallist Timothy Gowers called it "the first AI solution to a major problem outside his own field." Qiaochu Yuan called it "the most famous open problem solved by a language model so far." OpenAI's Codex reportedly found the same counterexample independently, which either validates the result or raises questions about how hard the search actually was, depending on who you ask. The skeptics have a point worth taking seriously. Andrew Blumberg argues a counterexample is fundamentally a search problem — generate candidates, check them, repeat — and that this reveals nothing about mathematical insight compared to constructing a proof. The counterexample is trivially verifiable once you have it; the hard part was the search space, which is exactly where raw compute wins. That's a real distinction. But the counterargument is also real: the conjecture fooled serious mathematicians for nearly a century. Beniamino Segre published three separate incorrect proofs. Claude Chevalley accepted a flawed one. The search space was large enough that humans never found this. Degree 7 versus degree 200 is not a small gap. Alpöge hints there may be a positive result hiding inside the counterexample structure, and a full write-up is coming. The two-variable version of the conjecture remains open. The meta-take forming in some corners: this is what AI-assisted math looks like in practice. Not replacing mathematicians, but dramatically compressing the search phase of disproofs. Expect a lot more of this. ## Questions this post answers ### What is the Jacobian conjecture and how was it disproved? The Jacobian conjecture, posed in 1939, claimed any polynomial map with a constant nonzero Jacobian determinant must be globally invertible. It was disproved with a cubic polynomial map from ℂ³ to itself, found by Anthropic mathematician Levent Alpöge working with Claude Fable 5, that sends three distinct input points to the same output while having a constant Jacobian determinant of −2 everywhere, making it non-invertible. _daily.dev surfaces how AI models are being applied to open problems in math and research._ ### What degree was the counterexample to the Jacobian conjecture, and why does that matter? The counterexample found by Claude Fable 5 uses polynomials of degree 7, far below the degree up to 200 that mathematicians had estimated would be needed to find any counterexample. This gap is seen as significant evidence of AI compressing a search space that had defeated human mathematicians for nearly a century, including flawed proof attempts by Beniamino Segre and Claude Chevalley. _developers weighing what AI search capability actually proves can follow this debate on daily.dev._ ## Similar posts on daily.dev - [A Simplified View of the Jacobian Conjecture](https://daily.dev/posts/a-simplified-view-of-the-jacobian-conjecture-31xgiqpq6) · Towards Data Science · 0 upvotes · 0 comments - [Human mathematicians are being outcounterexampled](https://daily.dev/posts/human-mathematicians-are-being-outcounterexampled-ocacgpf22) · Hacker News · 3 upvotes · 0 comments - [levent \(@\_\_alpoge\_\_\)](https://daily.dev/posts/levent-alpoge--tw81rka04) · Hacker News · 0 upvotes · 0 comments - [How I Vibed a Proof of Conway’s Conjecture — overreacted](https://daily.dev/posts/how-i-vibed-a-proof-of-conway-s-conjecture-overreacted-onrulhfhq) · Overreacted · 5 upvotes · 0 comments --- Tags: [#ai](https://daily.dev/tags/ai), [#claude](https://daily.dev/tags/claude), [#anthropic](https://daily.dev/tags/anthropic), [#math](https://daily.dev/tags/math) [View this post on daily.dev](https://daily.dev/posts/claude-fable-5-just-disproved-an-87-year-old-math-conjecture-by-prompting-uhggmvehq) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Claude 'Fable 5' just disproved an 87-year-old math conjecture by prompting","url":"https://daily.dev/posts/claude-fable-5-just-disproved-an-87-year-old-math-conjecture-by-prompting-uhggmvehq","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/claude-fable-5-just-disproved-an-87-year-old-math-conjecture-by-prompting-uhggmvehq"},"datePublished":"2026-07-21T13:34:36.459Z","dateModified":"2026-09-13T19:58:10.607Z","description":"An AI model called 'Claude Fable 5' reportedly produced a counterexample to the Jacobian conjecture, an open mathematical problem since 1939. 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