Hot on the heels of a flurry of cases of artificial intelligence furthering the field, OpenAI declared a major scalp: its latest AI model had cracked a Millennium Prize Problem, a puzzle with a $1m reward that had defied human brains for decades. The achievement bore little resemblance to how mathematical problems normally fall. A near-trillion dollar private company had unleashed 10,000 agents – AI systems that carry out tasks autonomously – on the problem.
The bill was estimated at $15m. The trajectory towards AI capable of superhuman maths has long been clear, but to nail such a substantial problem so swiftly sent shock waves through the field. Mathematicians are asking what will be left for themif works in progress are hoovered up and claimed by others, and how they should train the next generation when even fiendish assignments can be solved at the press of a button.
At a recent public lecture, she said she believed that AI was unlikely to do anything remarkable soon. It’s coming so fast.” Prof David Silvester, a mathematician at the University of Manchester, said the field felt “very unstable” given the pace of change. This is not going to change.” Prof James Robinson, a mathematician at the University of Warwick, said hard problems were the fuel of mathematics, driving creative approaches across successive generations.
For many mathematicians it is the weeks, months and years spent circling a problem, breaking it down, trying one approach after another, and never quitting that appeals. Mathematicians already devote considerable time to verifying each other’s proofs. It was this kind of review that found a gap in Andrew Wiles’s work on Fermat’s Last Theorem in 1993, prompting a year of further effort to fix the flaw.
Silvester suspects mathematicians might find themselves poring over ever more proofs dashed out by AI. There are knock-on effects throughout the field. Mathematicians are recruited on the strength of their published papers, but problems they have been working on for months might now be solved by AI in days.
Universities routinely set students problems and quizzes to work through at home. That kind of coursework is now dead. Lecturers are now having to tell students not to use AI for some problems, while ensuring they can use it for others: after all, AI-assisted maths is the future.
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