AI's solution to 87-year-old riddle takes mathematicians by surprise (www.newscientist.com)

In a remarkable development, mathematician Levent Alpöge, leveraging AI tools, has resolved the 87-year-old Jacobian conjecture, announcing his findings via a tweet. This conjecture, posed by Ott-Heinrich Keller in 1939, essentially questions whether certain mathematical functions can be reversed. Alpöge's concise proof, encapsulated in just 216 characters, has sent ripples through the mathematical community, particularly as it challenges a problem that was deemed one of the toughest on Stephen Smale's notable list from 1998. Noteworthy is that Alpöge credited the AI model Claude Fable 5 from Anthropic for aiding his research, although specifics on how the model was employed remain undisclosed. The implications of this breakthrough are profound, according to experts. Abhishek Saha emphasized that AI has shown unexpected prowess in mathematical problem-solving, with this achievement marking a significant milestone in the capabilities of AI in mathematics. As AI systems like Claude evolve, there's potential for them to tackle even more complex problems, raising questions about the future role of human mathematicians in the field. While the Jacobian conjecture has been disproven for three variables, discussions continue regarding its validity in other dimensions, ensuring that the excitement around AI's contributions to mathematics remains vibrant and full of possibilities.