Anthropic Mathematician Posts Counterexample to 1939 Jacobian Conjecture

Anthropic mathematician Levent Alpöge posted a hand-checkable counterexample to the Jacobian Conjecture on July 19, a problem open since 1939. Mathematicians had estimated any counterexample would need degree around 200, big enough that no one could check it by hand. Alpöge's version comes in at degree 7.

He and a collaborator named Matthew built it while working with Claude Fable 5: a degree-7 polynomial map in three variables with a constant Jacobian determinant of -2, yet three distinct points that land on the same output. That collision is exactly what the conjecture says can't happen.

The post hit Hacker News hard, 538 points and 334 comments in 11 hours. But the argument in the thread wasn't about the polynomial. It was about how much of the search Claude generated versus how much Alpöge and Matthew steered by hand, and the post doesn't settle that split.

A separate report elsewhere on Hacker News found AI advice can raise people's confidence while cutting their accuracy, from 27 percent down to 9 percent even as confidence rose from 30 to 76. That's the same problem from a different angle. It's hard to tell from outside a single post how much of a result is the model and how much is borrowed confidence.

Outside mathematicians haven't checked the credit split yet. When they do, expect Claude's share to shrink from 'found it' to 'searched a space Alpöge already knew to look in.'