Mathematicians grapple with a ‘very rapid and very unsettling change’ as AI cracks yet another century-old problem

Mathematics is witnessing a shift that experts describe as rapid and unsettling. This week, an artificial intelligence model solved the Jacobian conjecture, an 87-year-old mathematical problem first proposed in 1939. The result was verified by machine checking, effectively closing a case that long challenged human mathematicians.

The announcement came from Levant Alpöge, a researcher at Anthropic, and quickly moved through the mathematics community. While the solution provides the correct result, it highlights a tension between machine speed and human understanding. Mathematicians emphasize that while they can confirm the accuracy of the proof, the model provides the answer without the conceptual story that traditionally defines the discipline.

This development follows other recent milestones, including AI success at the International Mathematical Olympiad and the disproval of an Erdős conjecture earlier this year. These events have sparked conversations about the future of the profession, with researchers calling for guardrails around transparency and peer review as machines move into territory once reserved for the human mind.

Some experts argue that the true value of human mathematicians lies in their ability to pose the right questions rather than just calculating outcomes. As machines continue to resolve long-standing puzzles, the role of the mathematician moves toward that of a shepherd, watching as logic is applied at scales and speeds that go beyond human capacity. The industry remains divided on whether this shift democratizes the field or undermines the practice of pure mathematics.