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Mathematician and Anthropic employee Levent Alpöge presents an explicit counterexample to the Jacobian

AI boom — Mathematician and Anthropic employee Levent Alpöge presents an explicit counterexample to the Jacobian conjecture in three-dimensional space that disproves the <math>n</math>-varia

Published July 19, 2026· Updated October 28, 2026·1 min read

Context: AI boom.

Mathematician and Anthropic employee Levent Alpöge presents an explicit counterexample to the Jacobian conjecture in three-dimensional space that disproves the <math>n</math>-variable conjecture for <math>n > 2</math> using the large language model Fable 5. The Jacobian conjecture for <math>n = 1</math> remains true. [https://e.vnexpress.net/news/tech/tech-news/ai-helps-harvard-mathematician-crack-near-century-old-math-problem-5101182.html (VNexpress)] [https://www.newscientist.com/article/2580374-ais-solution-to-87-year-old-riddle-takes-mathematicians-by-surprise/ (NewScientist)]

Event summary via Wikipedia Current Events (2026-07-19).