Anthropic’s Claude Fable 5 and OpenAI Codex Generate Identical Counterexample to 87-Year Jacobian Conjecture
Anthropic researcher Levent Alpöge posted a polynomial counterexample that falsifies the Jacobian conjecture, a mathematical problem established in 1939. The proof was generated using Claude Fable 5, a language model from the Palo Alto artificial intelligence company. The conjecture remains one of the most prominent open problems in algebraic geometry, having resisted resolution for 87 years.
Researchers also reported that an internal version of OpenAI’s Codex model independently arrived at the same counterexample using a single text prompt and without access to the internet or external mathematical tools. The model’s output required no reinforcement learning or specialized proof-checking harnesses, and the original prompt has been shared publicly. The mathematical result has additionally been used to disprove several other related conjectures.
From the sources (25 posts)
@teortaxestexholy shit
@_arohan_RT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@teortaxestexFable predicts the LLM-powered disproof of the Jacobian conjecture by 2029–2032, 1-3 years before AGI, 2-6 before singularity. Faced with its success, it copes about "fabricated scenario from July 2026", then checks… «Condolences to Argent
@tszzlRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@boazbaraktcsWow! Congrats!
@ineratiRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@aidan_mclauRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@andrewcurran_RT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@scaling01drive-by humiliation of all mathematicians he disproved a 87 year old open math conjecture by prompting Fable and the counterexample is almost trivial
@teortaxestexKimi thinks for 24K tokens at <32 tps (vs Fable's 92 seconds at 60ish), fixates on irrelevant bullshit, drafts its response like a thesis, asserts it's Claude in CoT, also confirms the result. Fable is Impressed. «honestly, its verificat
@teortaxestexI don't think mathematicians should worry much yet if the first part of Levent's bio were true, then for sure
@8teapiRT @jdlichtman: This is quite a remarkable result: Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic…
@mlpoweredRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@tszzlit is pretty funny showing language models the Jacobian disproof and blowing their minds over and over again
@teortaxestexyou know, now I kind of wonder what Levent actually does for Anthropic, in the time not occupied by vibe-solving Smale's problems during the World Cup the 18th one is a really funny way to end the list
@emostaqueRT @jdlichtman: This is quite a remarkable result: Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic…
@callebtcRT @QiaochuYuan: for some background, 1) the jacobian conjecture is by far the most famous open problem resolved by an LLM so far 2) it'…
@timdarcetIn love with just giving this polynomial to an LLM with no context and innocently asking it "study" then watching its mind get blown in real time
@enzo_gteRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@ns123abc🚨 BREAKING: Jacobian Conjecture Proven False By AI One of the central open problems in algebraic geometry for 87 years has just been disproved by Anthropic researcher Levent Alpöge with Claude Fable 5 We're in a new age of science and pro
@dilipkayRT @__alpoge__: hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend f…
@daveaitelRT @jdlichtman: This is quite a remarkable result: Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic…
@gmoneynftwell thank god we solved the jacobian conjecture. i was really starting to get worried we wouldn't.
@mtsliveSITUATION BREWING: Anthropic researcher Levent Alpöge says the Jacobian conjecture, open since 1939, is false, posting an explicit polynomial counterexample. He credited Claude Fable 5 for helping.
@omarsar0What!? It looks correct. I am convinced we are not pushing these LLMs enough. Benchmarks are simply not enough. That’s exciting. Now can you please remove all the unnecessary guardrails from Fable so more of us can try solving extremely