“A mathematician has cracked an 87-year-old conundrum with the help of AI and announced the solution unceremoniously in a tweet. The finding is the most difficult mathematical problem yet solved by AI, say experts.

Levent Alpöge at Harvard University wrote on X on 19 July that the Jacobian conjecture – which academics have spent decades trying to prove was true – is actually false, giving a tiny, 216-character counterexample as proof…

The Jacobian conjecture – which suggests that a certain type of mathematical function would also work in reverse – was formally set out by Ott-Heinrich Keller in 1939. It was also on an influential list of 18 fiendishly difficult problems for mathematicians to tackle in the 21st century drawn up by Stephen Smale in 1998…

Abhishek Saha at Queen Mary University of London says AI’s recent advances in mathematics, such as the OpenAI model that recently cracked a decades-old conjecture by Paul Erdős, have been surprising, but this latest finding has stepped things up significantly.

'Probably this is the biggest conjecture that AI has played a significant role [in proving or disproving] so far in mathematics,' he says. 'This is a pretty big deal. AI has [made] remarkable progress in the last year.'

The single line of mathematics posted by Alpöge was simple to verify and many mathematicians have already done so, says Saha. Now the big question is how it was done.”

From New Scientist.