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Counterexample

2 articles · Page 1 of 1
IT Services Circle
IT Services Circle
Jul 21, 2026 · Artificial Intelligence

How Claude Fable 5 Disproved a 142‑Year‑Old Jacobian Conjecture with Three Simple Formulas

A mathematician named Levent Alpöge announced on X that Claude Fable 5 generated a three‑dimensional counterexample to the 142‑year‑old Jacobian Conjecture, which was instantly verified with Mathematica, updating the Wikipedia entry and highlighting AI’s growing role in solving deep mathematical problems.

AIClaude Fable 5Counterexample
0 likes · 9 min read
How Claude Fable 5 Disproved a 142‑Year‑Old Jacobian Conjecture with Three Simple Formulas
Machine Heart
Machine Heart
Jul 20, 2026 · Artificial Intelligence

One Tweet, One Counterexample: Did Claude Fable 5 Disprove the 85‑Year‑Old Jacobian Conjecture?

A tweet by Anthropic researcher Levent Alpoge, aided by the Claude Fable 5 model, presented a simple polynomial map whose constant Jacobian determinant of –2 sends three distinct points to the same image, providing a concrete counterexample that refutes the Jacobian conjecture that has challenged mathematicians for 85 years.

AI in mathematicsClaude Fable 5Counterexample
0 likes · 11 min read
One Tweet, One Counterexample: Did Claude Fable 5 Disprove the 85‑Year‑Old Jacobian Conjecture?