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.
at Harvard University that the Jacobian conjecture 鈥� which academics have spent decades trying to prove was true 鈥� is actually false, giving a tiny, 216-character counterexample as proof.
The 鈥� which suggests that a certain type of mathematical function would also work in reverse 鈥� 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.
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Alp枚ge did not respond to New 杏吧原创鈥檚 request for interview, but said in his tweet that part of the work was down to his 鈥渃lose friend fable鈥�- seemingly referring to AI company Anthropic鈥檚 Claude Fable 5. Alp枚ge thanked Fable for working during the World Cup final.
Anthropic did not respond to a request for comment.
聽at Queen Mary University of London says AI鈥檚 recent advances in mathematics, such as the OpenAI model that recently cracked a decades-old conjecture by Paul Erd艖s, have been surprising, but this latest finding has stepped things up significantly.
鈥淧robably this is the biggest conjecture that AI has played a significant role [in proving or disproving] so far in mathematics,鈥� he says. 鈥淭his is a pretty big deal. AI has [made] remarkable progress in the last year.鈥�
The single line of mathematics posted by Alp枚ge was simple to verify and many mathematicians have already done so, says Saha. Now the big question is how it was done.
鈥淭here are some problems that are very hard to solve but once a solution is there, they are relatively easy to check.鈥㏒o this is like that,鈥� he says. 鈥淚 don鈥檛 know how he did it, what exactly was the prompt to give Fable, because if one were to search everything, it wouldn鈥檛 quite work, so obviously there was some insight also which is not currently published.鈥�
Saha says both the appearance and the nature of the result is a surprise. 鈥淧eople have been trying to prove it [the Jacobian conjecture] because it sounds, intuitively, very true. I don鈥檛 think that many people have been trying to disprove it. And now we have this one-sentence counterexample,鈥� he says.
There are still open questions, says Saha. For example, this new counterexample disproves the conjecture with three variables, but a version with two variables could theoretically still be true.
at the University of York, UK, says mathematicians have in some ways already adjusted to the shocking new capabilities of AI, but there is a difference between finding counterexamples that disprove conjectures and building whole new branches of mathematics, which still requires human creativity.
鈥淚f you look at Fermat鈥檚 last theorem [which was solved by Andrew Wiles in 1994], you had to create a hundred pages of new mathematics 鈥� you had to build a whole big theory in order to solve a conjecture,鈥� says Bowman-Scargill. 鈥淎nd often the interesting stuff in maths isn鈥檛 鈥榦h, we鈥檝e ticked off this conjecture, yay鈥�, it鈥檚 more the stuff you have to build along the way in order to solve the conjecture.鈥�
鈥淚 think [AI] has sort of proven that it can do this, so you鈥檙e now like, OK, what next?,鈥� he says.
at Westlake University in China believes what comes next is increasingly capable AI models that will solve ever more complex problems, disrupting the field as they go.
鈥淩ight now, AI can already produce master鈥檚 degrees in mathematics. In one year, they will produce PhD degrees in mathematics. And then the question arises, do we really need so many mathematicians around if AI can do such things so nicely?鈥� says Fesenko. 鈥淪o basically we鈥檙e talking about fundamental change in mathematics.鈥�
