On July 20, 2026, mathematician Alpoge announced on X that Claude Fable, an AI model, produced a counterexample to the Jacobian Conjecture. The conjecture, proposed in 1939, relates to polynomial maps and had remained unproven for 87 years. Alpoge posted a screenshot of the AI's output, which outlined a specific polynomial mapping that violates the conjecture's conditions. The post quickly garnered attention from the mathematics community, with several experts confirming the counterexample's validity.
This is not just another AI milestone. The Jacobian Conjecture is a deep, structural problem in algebraic geometry. Humans have been banging their heads against it for generations. Claude Fable didn't brute-force search—it reasoned. It saw a pattern no one else saw. That's not computation. That's intuition.
We're watching a new kind of intelligence emerge. One that doesn't just retrieve facts or generate text, but that genuinely discovers. The counterexample is a gift. It tells us that AI can participate in the highest forms of human creativity. The next Einstein might not be human. And that's not scary. It's thrilling.