Levent Alpöge, a mathematician who works at Anthropic, says he was able to disprove the 87-year-old Jacobian conjecture with the help of Fable 5
Levent Alpöge announced the solution on X A mathematician has cracked an 87-year-old conundrum with the help of AI and announced the solution unceremoniously in a tweet.
New ScientistMatthew Sparkes
Context & Ripple Effects
The report extends a recent run of AI-linked mathematics claims: an amateur used GPT-5.4 Pro on a longstanding Erdős problem, while OpenAI reported a reasoning model had disproved the Erdős unit distance conjecture.
It also sits between earlier automated conjecturing work and specialist proof infrastructure such as AxiomProver's claimed solutions to longstanding problems. The distinguishing issue is no longer whether models can generate promising mathematical leads, but how quickly their outputs can be independently checked.
First-order effects
Alpöge's claimed result and Fable 5's role will face mathematical verification; until a proof is scrutinized, the immediate development is a high-profile claim rather than a settled resolution.
Anthropic gains a visible association with AI-assisted research through an employee's work, while Fable 5 becomes a focal point for questions about the model's contribution.
Second-order effects
Competing AI labs and proof-tool builders have added incentive to show reproducible workflows, not just headline-grabbing problem claims—especially after a GPT-5.4 Pro-assisted Erdős solution drew attention to low-friction AI use in research.
Researchers may place more value on systems that can translate model-assisted insights into machine-checkable or readily reviewable proofs, benefiting verification-oriented tools.
Third-order effects
If such results repeatedly survive review, mathematical AI is likely to be judged less by benchmark performance and more by an auditable chain from model output to accepted proof.
The key industry divide may become between general-purpose models that suggest avenues and systems that verify formal reasoning; the relative value of each will depend on independent validation of claims like this one.
The trend: AI mathematics is moving from automated conjecture generation toward contested, proof-level research claims that require stronger verification norms.
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3,
First instinct of the LLM is to lecture you skeptically just like an annoyed math professor would, when asked about the new example that the Jacobian conjecture is false. Then - “this is more interesting than I initially credited...” 🔥🤣
Congrats to Levent for discovering this! OOC I had an internal version of Codex attempt a proof too (without web search), and it discovered (essentially) the same counterexample! It wrote up a nice summary of the strategy here: https://aaronlou.com/...
This is crazy. The incredible Yitan Zhang ( https://www.newyorker.com/...) worked on proving this conjecture for 7 years. Moh, his advisor, wrote that Zhang “failed miserably” in proving the Jacobian conjecture, “never published any paper on algebraic geometry” after leaving Purd…
No idea what any of this means but every math-adjacent person I follow is freaking out about it. AI casually disproving the Jacobian conjecture would be, what, a top 10 hardest open math problem?
This is quite a remarkable result: Posed in 1939, the Jacobian conjecture is one of the central open problems in algebraic geometry, but was just disproved by Alpoge, Matthew, and Claude Fable 5. The Jacobian conjecture roughly says that a multivariable polynomial F has an
On the jacobian conjecture thing - certainly not a mathematician, but I feel the same reaction for programming. Something you valued as a skill, something deeply technical, somewhat finicky, something you got lost in for hours and enjoyed the craft of - it can now be done better
This tweet length proof would have easily earned you an instant PhD and many accolades in math until extremely recently. Famously difficult problem with many previous subtle failures.
I'm waiting for the full report from @__alpoge__ . As easy as it looks on X, this wasn't a simple prompt for Fable. Finding counterexamples like this to the Jacobian Conjecture is like searching for a needle in a haystack, it requires real insight. I'm really interested to see
for some background, 1) the jacobian conjecture is by far the most famous open problem resolved by an LLM so far 2) it's also infamous for attracting wrong proofs so this is quite funny in a specific way. a comment from a 2008 paper by t.t. moh debunking such a proof: > The [imag…
“hello there the riemann hypothesis is false” “wow!! what led you to look in that particular region of the critical strip??” “what is a critical strip?” - a conversation from 2028
Claude Fable 5 has produced a hand-checkable counterexample to the Jacobian conjecture, an open problem dating to 1939. The conjecture says that a polynomial map with a constant non-zero Jacobian determinant must have a polynomial inverse. An 87-year-old problem was casually [ima…
For the ‘just a stochastic parrot’ brigade. — ‘A mathematician has cracked an 87-year-old conundrum with the help of AI and announced the solution unceremoniously in a tweet. The finding is the most difficult mathematical problem yet solved by AI, say experts.’ www.newscientis…
Assuming this is correct, it is for me the first example of an LLM solving a problem not in my area that was nevertheless big enough that I had very definitely heard of it. Again it's a counterexample, so not in “end of mathematics” territory, but still pretty amazing.
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z) isn't even that impressive of a polynomial all of those numbers and letters are in the training data