Claude's Fable 5 Just Solved an 87-Year-Old Math Problem, and It Matters for Bitcoin
Levent Alpége and Anthropic’s Fable 5 found a three-dimensional counterexample, and researchers said AI can search huge polynomial spaces humans cannot.
- On Sunday, July 19, 2026, Harvard fellow Levent Alp announced he used Anthropic's Fable 5 model to disprove the Jacobian conjecture, a problem that defied mathematicians for 87 years.
- First proposed by Ott-Heinrich Keller in 1939, the conjecture asks whether polynomial maps with non-zero Jacobian determinants are reversible; Stephen Smale included it on his influential 1998 list of 21st-century challenges.
- Fable 5 generated a map from three-dimensional space to itself that passes the reversibility check but cannot be reversed because three different inputs yield the same output, disproving the Jacobian rule with one counterexample.
- Columbia University mathematician Andrew Blumberg noted the achievement is significant but the counterexample offers limited insight compared to a full disproof, while Fields medalist Timothy Gowers acknowledged the milestone yet cautioned it lacks theoretical depth.
- This capability leap strengthens the case for pouring capital into AI development, posing a conundrum for investors as AI's steep capability curve draws market risk appetite away from speculative assets.
14 Articles
14 Articles
AI just disproved the 87-year-old Jacobian conjecture
On Sunday evening, as Spain and Argentina played out the World Cup final, the mathematician Levent Alpöge posted a short message on X. The Jacobian conjecture, he wrote, is false. He thanked a friend for asking about it, and another friend, “fable,” for working during the match. That second friend was Fable 5, Anthropic’s latest […] This story continues at The Next Web
AI just disproved a major math problem. A mathematician explains.
The Jacobian conjecture has bedeviled math experts for nearly 90 years. While the rest of the world was watching the World Cup on Sunday evening, mathematician Levent Alpöge casually announced on X that he had used Anthropic's Fable 5 to disprove the Jacobian conjecture. The Jacobian conjecture is a long-standing open problem in algebraic geometry …
Claude Fable 5, a model of Anthropic, helped find a counterexample that refutes Jacobian's conjecture, an open mathematical problem since 1939. The advance also exposes how attention and speculative capital move away from Bitcoin to concentrate on AI, chips and computing ability. *** Claude Fable 5 helped refute Jacobian's conjecture, in force for 87 years. The model proposed a mathematical machine that exceeds standard verification, but cannot …
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