AI helps solve difficult problems that have existed for nearly 90 years

Levent Alpoge says the hypothesis is essentially wrong and proves it with a brief example, discovered with the help of Anthropic's Claude Fable model. His Twitter post attracted 30 million views, 41,000 likes and a series of comments in less than three days. Many experts consider this to be the most difficult problem that AI has ever helped solve.

According to Fast Company, the Jacobian hypothesis, proposed by German mathematician Eduard Ott-Heinrich Keller in 1939, states that if we start with a point on a coordinate grid represented by ordinary variables (such as x and y), then use a polynomial - an equation containing powers such as x² or y³ - to create new coordinates, then we can reverse that process by using polynomials and restore the original coordinates. The Jacobian hypothesis is on the list of 18 super difficult problems to solve in the 21st century created by mathematician Stephen Smale in 1998.

Alpoge's counterexample is only 216 characters long and has not undergone peer review, but several mathematicians have reportedly confirmed the calculation and independently tested it using SymPy (a Python library for symbolic mathematics) and Lean (a theorem-proving tool). Many others also use AI support, including OpenAI's GPT, for their own verification.

Abhishek Saha, a mathematics professor at Queen Mary University of London, said recent advances in AI in mathematics were already surprising, but the latest achievement takes things to the next level. "To date, this is probably the biggest mathematical hypothesis that AI has played a significant role in proving or disproving," he told New Scientist.

If confirmed, Alpoge's findings could provide one of the strongest evidence to date of what AI developers often claim: advanced models will dramatically accelerate mathematical and scientific discovery. The new achievement could also challenge those who believe AI is not useful in fields that require high precision.

Chris Bowman-Scargill, a PhD at the University of York (UK), believes that mathematicians have somewhat adapted to AI's impressive capabilities. However, he emphasized that there is still a difference between finding a counterexample to disprove a hypothesis and building a completely new branch of mathematics, which requires human creativity. "The interesting thing in mathematics is often not 'oh, we've solved this conjecture', but the things you have to build on the way to solving that conjecture," he said.