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Mathematicians despair at AI’s stunning breakthroughs - mklabgr - 08-16-2026
Mathematicians despair at AI’s stunning breakthroughs
Field vulnerable to tech developments because of its theoretical nature
By James Titcomb
Field vulnerable to tech developments because of its theoretical nature
By James Titcomb
AI takes on the Riemann hypothesis
Jared Sumner, an engineer at AI company Anthropic, was out jogging when he briefly stopped to type something into Claude.
Sumner asked the bot to “take a real stab” at solving the Riemann hypothesis – a 167-year-old mathematics puzzle that has perplexed the field’s experts ever since.
Solving it would be one of maths’s biggest breakthroughs in decades, and net a million-dollar prize. Over the next day and a half, Sumner – who is not a mathematician – acted as cheerleader, telling the bot to keep going.
Quote:“You got this,” he told it.Claude did not solve the hypothesis, which seeks to unlock the patterns governing prime numbers.
But on a related test, it got further than any human ever has.
A meaningful development and a result that was just the latest case of AI making a major maths breakthrough.
Quote:“In the span of about half a year, it went from not being able to count to solving problems we spend years [on].”
AI breakthroughs are accelerating
The result was not a one-off. In July, Claude was used to disprove the Jacobian conjecture, an 87-year-old geometry theory. Levent Alpöge, the Anthropic employee who had made the discovery, had set the AI to work during the turgid World Cup final.
Rival company OpenAI said this month a new model made 10 maths discoveries in a week.
A series of famous riddles left by Paul Erdős, a celebrated Hungarian mathematician, were solved by AI in the last year.
Mathematicians have greeted these developments with a mixture of despair, disbelief and excitement.
Quote:“Some are going through the five stages of grief,” says Kevin Buzzard, a maths professor at Imperial College London.Buzzard says he is excited about the prospect of a flurry of breakthroughs, but admits: “I do wonder whether I’m in a suffering a profound spiritual crisis due to these developments,” Kirwin Hampshire, at the University of Victoria in Canada, wrote in a recent viral essay.
Quote:“I feel as though I am living inside of a nightmare.”
The danger of delegating mathematical thinking
Giorgio Navone, a PhD student at University College London, says it is tempting for students to reach for the tools at the expense of their own development.
Quote:“It’s very risky to basically delegate your thinking to AI. It gives the impression of really quick progress but you don’t generate the knowledge for yourself.”Plenty of disciplines – from taxi drivers to illustrators – are worried that AI could make them obsolete. But maths is seen as especially vulnerable due to its theoretical nature, which means there are no lab tests to be done or prototypes to deploy.
Quote:“It’s a game that you … play in your head,” says Buzzard. “If AI can easily verify it is what makes it amenable to this disruption.”Buzzard says AI’s ability to absorb enormous quantities of information makes it particularly well suited to maths discoveries.
Quote:“It’s been over 100 years since a human could know all of mathematics. AI can somehow become extremely knowledgeable in several domains at the same time.”
What happens to the role of mathematicians?
The romance associated with being the first person to solve a famous and long-standing unsolved problem, says Sir Tim Gowers, a Cambridge professor who won the prestigious Fields maths prize in 1998.
Quote:“If [AI means] the job of mathematicians is to explain and interpret AI discoveries, then it will be less appealing to many.”It is not all bad news. The ability of AI to verify a solution to a problem he had spent a long time considering, meaning the AI had answered on the first attempt.
Quote:“It felt very strange and not particularly pleasant to have the rug pulled out from under my feet like that,” he wrote on his blog.
A backlash from the mathematics community
Alex Gerko, the Russian-born British billionaire and mathematician behind trading firm XTX Markets, suggested some AI researchers disrespected the field by breezily revealing jaw-dropping results they had asked for while watching football or jogging.
Quote:“Does anyone else find the tone of Anthropic people announcing major maths discoveries jarring?”There is now an organised backlash from the maths world. More than 3,500 people have signed a declaration warning that AI can create plausible-sounding but inaccurate results and that the technology could lead universities to cut funding for maths.
Others are saying it may be time to join them. Jacob Tsimerman, who won the Fields medal this year, used the awards ceremony to announce he was joining OpenAI, saying AI would soon become superhuman at mathematics and he wanted to dedicate his life to making the systems safer.
“50 years’ worth of maths progress”
Gerko, meanwhile, has predicted a wave of mathematical discoveries.
Quote:“We are going to see 50 years’ worth of maths progress in the next two years,” he wrote. “But there won’t be nearly enough mathematicians around to process and understand all of it.”
Artificial intelligence may not replace mathematicians, but its rapidly growing ability to discover, verify and explore mathematics is forcing the field to reconsider what mathematical research — and the role of the mathematician — could look like in the coming years.
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