An AI agent appears to have disproved one of mathematics' most famous open conjectures, and the math world is debating it live

An AI May Have Disproved a Famous Math Conjecture. Nobody Can Quickly Check the Answer.

Overnight, mathematician Levent Alpoge posted what he described as a counterexample to the Jacobian Conjecture, an open problem in algebraic geometry posed in 1939 that has attracted so many false proofs over the decades that Alpoge himself described it as "the canonical crank graveyard" 1.

The counterexample was not Alpoge's own work. He credited it to "fable," meaning Claude Fable, an AI assistant made by Anthropic 2. The claim is concrete: a polynomial map from three-dimensional complex space to itself, with a Jacobian determinant that Alpoge verified equals a constant -2 using Wolfram Alpha. He listed three distinct input points, (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2), that the map sends to the same output: (-1/4, 0, 0). If those three points truly collapse to one under a map whose Jacobian is a nonzero constant, the Jacobian Conjecture's central claim fails 1.

Hours later, nobody had confirmed it. The reply thread had become a live refereeing session. Daniel Litt, a mathematician at the University of Toronto, asked for details on how the counterexample was found 1. One commenter raised a pointed technical objection: over the complex numbers, the counterexample needs to satisfy a properness condition, and it was unclear whether the example Alpoge posted does 1. Others asked for the reasoning traces that led the AI to the result. Alpoge had not shared them.

The Jacobian Conjecture, stripped of its technical machinery, makes a deceptively simple claim: if a polynomial map from n-dimensional space to n-dimensional space has a Jacobian determinant that is a nonzero constant everywhere, that map must be one-to-one. The Jacobian measures how a transformation distorts space locally. A constant nonzero value means no local collapsing or folding. The conjecture says that is enough to guarantee the map never sends two distinct inputs to the same output 1. Alpoge's example purports to show exactly that happening.

False counterexamples to the Jacobian Conjecture are practically a genre, which is why the community's skepticism is reflexive rather than dismissive. What is new here is the source. When a human mathematician proposes a counterexample, peers can ask how they found it and trace the reasoning back to its foundations. When an AI produces one, the discovery process is opaque. The model's internal computation does not map onto anything a mathematician would recognize as a deliberate strategy. Multiple researchers in the thread asked for prompts, traces, and methodology. The candidate answer exists. The reasoning behind it does not, in any form the community can inspect 1.

This is the structural problem, and it is not confined to mathematics. AI systems are now generating claims at the frontier of fields where verification is expensive, slow, and dependent on scarce expertise. Drug discovery, materials science, economic modeling: each has its own Jacobian Conjecture, a hard problem where the cost of checking an answer vastly exceeds the cost of producing one. When that gap opens, the institutions that adjudicate knowledge, peer review, replication studies, expert consensus, face a throughput crisis they were not built to handle.

Alpoge noted that Fable was "working during the world cup final" 1. The casualness captures the asymmetry. An AI system produced a candidate resolution to a problem that has stood open since 1939 in the span of a soccer match. The mathematical community's verification apparatus works on a different clock entirely, and it has no established protocol for adjudicating a claim whose reasoning it cannot examine.

The counterexample may hold. It may collapse under scrutiny, like the countless others that preceded it. Either way, the live debate it triggered, with mathematicians crowdsourcing verification in real time across social media, is the real test case. The question facing every field AI now touches is the same one algebraic geometry confronted overnight: when a machine can generate a frontier claim faster than experts can verify it, the bottleneck stops being discovery. It becomes trust. And the institutions built to produce trust were designed for a world where generating claims was the hard part.