Full story
AI cracks Jacobian conjecture
An Anthropic AI model, Claude Fable 5, helped disprove the Jacobian conjecture, an 87-year-old problem open since 1939, according to posts and reporting tied to the result.
“On this day, the entire global mathematics community was stunned”
Levent Alpöge, a number theorist who works at Anthropic, credited Claude Fable 5 and posted the counterexample on X on Sunday night, writing: "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".
The counterexample centers on a polynomial map from three-dimensional complex space to itself, with a Jacobian determinant of −2 everywhere, while three distinct inputs land on the same output point, making the map non-invertible.
Fortune reported that by the time Kevin Buzzard woke up in London the next morning, the result had been verified, and Buzzard said, "It is a big day".
Fortune also described how the result met the Jacobian determinant condition at every point yet still failed the global invertibility test, leaving the conjecture’s “local to global” promise broken.
Verification, peer review, and voices
While other mathematicians reproduced the algebra within hours, multiple outlets emphasized that no journal had refereed the work, and the two-variable case remains open.
Fortune quoted Akhil Mathew, the University of Chicago mathematician who Alpöge credits with suggesting the problem, saying, "One can check out that it’s correct," but adding that it would be better to "tell a story."
New Scientist reported that Abhishek Saha at Queen Mary University of London said the finding is "Probably this is the biggest conjecture that AI has played a significant role [in proving or disproving] so far in mathematics," and called it "a pretty big deal."
New Scientist also noted that Alpöge did not respond to an interview request, but said in his tweet that part of the work was down to his "close friend fable" and thanked Fable for working during the World Cup final.
In the same coverage, Chris Bowman-Scargill at the University of York said there is a difference between finding counterexamples and building whole new branches of mathematics, describing how Fermat’s last theorem required "a hundred pages of new mathematics".
Why it matters beyond math
Beyond the conjecture itself, the result was framed as a sign of how quickly AI can generate verifiable mathematics, with multiple sources pointing to the World Cup timing and the ability to check the counterexample by hand.
“An 87-year-old classic problem that has stumped countless top mathematicians—the Jacobian Conjecture—may have been completely overturned by a three-line formula generated by Anthropic's AI model Claude Fable 5”
CoinDesk linked the breakthrough to markets, saying Claude Fable 5’s disproof “matters for bitcoin” because Bitcoin had been trading on AI narratives, and it described the counterexample as something mathematicians could verify by hand within a day.
CoinDesk also tied the timing to crypto’s recent volatility, noting that Bitcoin fell hard last Friday when Moonshot AI released a model that rattled the semiconductor industry, and then recovered as those stocks bounced.
Bitget similarly argued that each result like Fable’s finding strengthens the case for capital flowing into AI, while posing a conundrum for crypto investors about why hold a token that trades as a sidecar to the AI cycle.
In parallel, Fortune described the broader shift in mathematics as a “very rapid and very unsettling change,” with Buzzard and others describing how AI can reach conclusions while leaving mathematicians wanting the deeper “why” behind them.
%2Fhttps%3A%2F%2Fi.s3.glbimg.com%2Fv1%2FAUTH_63b422c2caee4269b8b34177e8876b93%2Finternal_photos%2Fbs%2F2026%2FY%2FQ%2FvThFmBTwSlL6QYgbK7UQ%2Ffoto21bra-301-queima-a2.jpg&w=3840&q=75)
