‘Immaiture playground boastin’: Mathematicians uneasy at OpenAI’s latest scalp

It wis a week that left mathematicians reelan. Follaein a wheen o cases o artificial intelligence forderin the field, OpenAI declarit a major scalp: its latest AI model had crackit a Millennium Prize Problem, a puzzle wi a $1m reward that had defied human brains for decades.

The achievement bore wee resemblance to hou mathematical problems ordinar hae a habit o fawin. A near-trillion dollar private company had unleashed 10,000 agents – AI systems that cairry oot tasks on their ain – on the problem. The bill wis estimatit at $15m.

The trajectory towards AI capable o superhuman maths has lang been clear, but to nail sic a substantial problem sae swiftly sent shock waves throu the field. Mathematicians are speirin whit will be left for them gin warks in progress are hoovered up and claimit by ithers, and hou they shud train the next generation whan even fiendish assignments can be solved at the press o a button.

“I feel slichtly shell-shockit,” said Prof Colva Roney-Dougal, the heid o pure mathematics at the University o St Andrews. At a recent public lecture, she said she believit that AI wis unlikely to dae onything remarkable seen. “Three months later, I am totally wrang,” she says. “We are a aw juist waitin to see whit happens. It is comin sae fast.”

Prof David Silvester, a mathematician at the University o Manchester, said the field felt “very unstable” gien the pace o chynge. “A the open maths problems cud faw wi enough resources,” he said. “This is irreversible. This is no gaun to chynge.”

Prof James Robinson, a mathematician at the University o Warwick, said hard problems were the fuel o mathematics, drivin creative approaches across successive generations. “It is frustratin to see these big tech companies burnin this fuel up juist sae that they can shaw aff aboot hou great their latest model is,” he said. “It seems like immaiture playground boastin writ lairge, underpinned by billions o dollars and the potential for significant environmental damage in an age whan climate chynge is probably the biggest challenge we face.”

Ane reason Silvester gaed into maths wis the rush that comes frae crackin a problem. For mony mathematicians it is the weeks, months and years spent circlin a problem, brakin it doun, tryin ane approach efter anither, and never quittin that appeals. “Without that, the subject seems completely different to me,” Silvester said.

Mathematicians already devote considerable time to verifyin ilk anither’s proofs. It wis this kind o review that fand a gap in Andrew Wiles’s wark on Fermat’s Last Theorem in 1993, promptin a year o further effort to fix the flaw. Silvester suspects mathematicians micht find theirsels porin ower ever mair proofs dashed oot by AI. “It is mair like becomin an accountant, ye are auditin, ye are checkin,” he said.

There are knock-on effects throuoot the field. Mathematicians are recruitit on the strenth o their publishit papers, but problems they hae been workin on for months micht nou be solved by AI in days. “There is a real sense o ‘I cud spend the next month thinkin aboot something and somebody else does it by pushin a button’,” says Roney-Dougal. “That is horrible, and I think it is gaun to be horrible for a few years.”

It is also a heidache for teachin undergraduates. Universities routinely set students problems and quizzes to wark throu at hame. That kind o coursework is nou deid. “There is nae point in doin it because we canna vouch for its authenticity,” says Silvester. Lecturers are nou haein to tell students no to use AI for some problems, while ensurin they can use it for ithers: efter a, AI-assistit maths is the future.

For a the upheaval, Prof Alexander Paseau, wha studies the philosophy o mathematics at the University o Oxford, believes maths will no lose muckle o its appeal. “The challenge still remains, even gin AI is eventually better than humans at research,” he said. “Ye will still want to be able to understand the mathematics yoursels. And we will still enjoy it and appreciate its beauty: the sheer enjoyment and the beauty o a mathematical proof will aye be there. AI is no gaun to tak ony o that awa.”

A lot o AI maths does no solve problems frae scratch, but builds on wark by humans, he addit. The OpenAI breakthrough, for example, relied heavily on wark by the Madrid-based mathematicians Diego Córdoba and Luis Martinez-Zoroa.

OpenAI’s wark describit a solution to the Navier-Stokes problem which involves equations that predict hou fluids, and even the weather, behave. It is ane o seven Millennium Prize Problems publishit by the Clay Mathematics Institute in 2000. The company’s announcement on Tuesday has led to further concerns in the community. OpenAI set its latest model to wark efter hearin rumours that twa Millennium Problems had been solved by mathematicians. Prof Tristan Buckmaster at New York University and Levent Alpöge at Anthropic were doin relatit wark on Navier-Stokes and had used OpenAI’s products in the process. They suspectit OpenAI’s model had learnit frae their wark-in-progress. Efter an investigation, OpenAI deniet this wis the case.

Some mathematicians are still wary, houever. “The big story nou in mathematics is that naebody wants to share onything,” Buckmaster tauld the Guardian. “Mathematics is different the day than it wis only a few days ago. We hae to decide whit to dae aboot that.”