For decades, the deepest open problems in mathematics have been the preserve of a handful of human experts. Solving one requires intuition, decades of domain knowledge, and the stamina to wrestle with abstractions that no machine learning system was ever designed to handle. That assumption was shaken recently, when an AI system appeared to produce a counterexample to a conjecture that had stood for nearly ninety years.
Proposed in 1939, the Jacobian Conjecture is a deceptively simple question about polynomials — expressions built from variables multiplied and added together, like the algebra you learn in high school, only far more elaborate. It asks whether a certain smooth kind of polynomial transformation can always be reversed. Despite its elementary statement, the problem has resisted the best minds in algebraic geometry for almost nine decades and was listed by mathematician Steve Smale among the most significant open problems of the 21st century.
A counterexample of this kind, if correct, would be a genuine landmark. But mathematicians reacted with healthy skepticism, and for good reason. AI systems are remarkably good at generating plausible-looking mathematics, yet they also confidently produce elegant falsehoods. The claim triggered a rare public audit: top researchers, including Fields Medalist Terence Tao, examined the output and the reasoning behind it.
Tao, who has called the Jacobian Conjecture one of his favorite open problems, walked through the claimed counterexample in detail and even shared a conversation with a chat model to help verify parts of the calculation. The episode became a case study in how the mathematical community adapts: rather than outright dismissal, experts are learning to use AI as a fast, fallible hypothesis generator that still needs a careful human referee.
Whether Fable 5's counterexample ultimately holds up is still being settled. Either way, the moment marks a quiet turning point: the day AI moved from helping mathematicians to competing with them on problems that even the world's leading thinkers had not solved.