# Anthropic mathematician uses Claude to find Jacobian conjecture counterexample above two dimensions

_Saturday, August 1, 2026 at 8:11 AM EDT · AI, Science · Latest · Tier 2 — Notable_

SciTechDaily, adapting an article originally published in The Conversation, reported that Levent Alpöge, a mathematician at Anthropic, announced a counterexample to the Jacobian conjecture found with help from Anthropic's large language model Claude Fable 5.

The Jacobian conjecture, generalized to any number of dimensions by Ott-Heinrich Keller in 1939 after a two-dimensional statement by Ludwig Kraus in 1884, says that a polynomial mapping whose Jacobian determinant is a non-zero constant should always have a polynomial inverse. Many claimed proofs over decades failed under scrutiny, while restricted cases and two-dimensional computational checks up to high degree supported the statement.

Alpöge found a short three-dimensional polynomial function with constant Jacobian determinant of -2 that sends multiple input points to the same output, so it is not reversible. SciTechDaily said the example is short enough to fit in a single post on X and was easy for other mathematicians to verify. The result shows the conjecture is false for every dimension larger than 2, while the original two-dimensional form remains open.

The writeup places the find alongside other recent AI-linked math results, including OpenAI's disproof of the unit distance conjecture and a proof of Erdos problem 1196 by amateur mathematician Liam Price, and notes AI's value in searching large spaces of candidate objects as well as constructing proofs.

Implication: A verified higher-dimensional counterexample narrows a century-old algebra problem and highlights AI search as a tool for finding mathematical objects.

## Sources

- [SciTechDaily](https://scitechdaily.com/ai-helps-crack-an-87-year-old-math-conjecture-with-one-tiny-formula/)

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