AI Solves a Famous Mathematical Problem That Remained Unresolved for 87 Years in No Time

While millions of people were watching the World Cup final between Spain and Argentina, a discovery took place in the world of mathematics that is sure to stir debate. Mathematician Levent Alpöge announced on X that the Jacobian Conjecture, a problem that has remained unresolved for nearly 90 years, has been proven false thanks to collaboration with an artificial intelligence model.

The decisive contribution came from Fable 5, the latest advanced model developed by Anthropic. The system, working alongside Alpöge, identified a counterexample just a few hundred characters long capable of challenging one of the most well-known issues in modern mathematics. The Jacobian Conjecture dates back to 1939 and concerns specific polynomial transformations.

In simplified terms, it claimed that a mathematical function with certain characteristics, including a constant non-zero Jacobian matrix determinant, must always have an inverse of the same type. Over the years, the problem had become one of the great open challenges in the discipline, so much so that Stephen Smale included it among the most important mathematical questions of the new millennium. The result obtained by the AI does not represent a complete proof but is a sufficient element to refute the theory: finding even a single valid case where the statement does not hold is indeed enough to render the conjecture false.

AI Solves the Jacobian Conjecture, the Unresolved Mathematical Problem for 90 Years

According to several mathematicians, the value of the discovery lies mainly in the ability of artificial intelligence to explore huge quantities of possibilities that are difficult to analyze manually. However, some experts have downplayed the impact of the news. Andrew Blumberg, a mathematician at Columbia University, pointed out that identifying a counterexample is very different from constructing a theory capable of explaining a phenomenon.

Other scholars, on the other hand, welcomed the discovery enthusiastically. Timothy Gowers, a Fields Medal winner, described it as astonishing that an artificial intelligence had solved a mathematical problem significant enough to be known outside its own specialization.

The episode represents a new example of the growing role of AI in scientific research. According to reports, even an internal model from OpenAI has independently found a similar counterexample. However, the story may not be concluded. Alpöge hinted that the analysis of the result could reveal hidden positive aspects and that a more detailed publication will follow.