This is one of those stories where it's worth pausing for a moment.

The Jacobian Conjecture is not an obscure niche corner of mathematics. It is a problem formulated in 1939 that has survived generations of the world's best mathematicians, and it appears on the list of major unsolved problems in algebraic geometry. The conjecture, broadly speaking, concerns when polynomial maps in multiple variables are invertible — and it has resisted both proof and disproof for nearly nine decades.

Mathematician Levent Alpöge now reports that he used Anthropic's latest model, Claude Fable 5, to find a concrete counterexample. In other words: the conjecture is false.

This isn't AI solving math on its own — it's AI spotting a pattern in a search space humans never had the chance to explore.

That distinction matters. Andrew Blumberg at Columbia has already commented that this is "exactly the kind of thing" AI is expected to contribute — finding compact counterexamples in vast search spaces where human intuition falls short. The claim isn't that the model "understands" mathematics the way a researcher does, but that it can navigate an enormous parameter space quickly and systematically.

The context makes it even more striking: Claude Opus 4.5 scored below 10% on FrontierMath Tier 4 earlier in 2026. Fable 5 scores 88%. That is not incremental progress — it is a quantum leap achieved in a matter of months.

AI cracks 90-year-old math problem no one could solve - Bilde 1

The HN thread is now buzzing with debate over whether this actually holds up mathematically, what it means for formal verification, and whether Lean or Coq should be used to check the result independently. That is exactly the right conversation to be having. Community consensus appears cautiously optimistic, but no one has dismissed it as nonsense yet.

It is worth noting that this is an early signal based on community sources and non-peer-reviewed material as of now. However, reactions from named mathematicians with credible institutional affiliations lend this more weight than most claims of this kind.

If it holds up, this is not merely a technical milestone. It is a signal that AI-assisted mathematics is moving from "useful tool" to "co-discoverer" — and that the pace of that transition is faster than most people had anticipated.

Keep an eye on the HN thread and watch for Alpöge to post a preprint.