{"slug": "a-human-set-a-new-mathematical-record-then-ai-came-for-it", "title": "A human set a new mathematical record. Then AI came for it", "summary": "Julia Stadlmann of the University of Illinois Urbana–Champaign set a new record on the twin prime conjecture on the last day of August, the first advance on the problem in more than a decade, only to be surpassed within three days by AI startup Axiom Math and then within two hours by OpenAI, which five days later claimed to have solved another major math puzzle. Stadlmann's result lowered the small prime-gap bound that had stood at 246 since mid-2014, following Yitang Zhang's 2013 proof that some prime gaps repeat infinitely. UCLA Fields Medalist Terence Tao wrote on mathstodon.xyz that the episode reflects \"some very deliberate choices to abandon any pretense of gaining human understanding … and using AI tools for the sole purpose of achieving a benchmark.", "body_md": "On the last day of August, a human mathematician kicked off a flurry of advances on one of the most famous problems in number theory — and was almost instantly superseded by AI.\n\nJulia Stadlmann of the University of Illinois Urbana–Champaign reported a new record in the quest to solve the twin prime conjecture, which posits that there are infinitely many pairs of prime numbers that are just two numbers apart (3 and 5 are twin primes, for example, as are 17 and 19). It was the first such advance in more than a decade.\n\nIt’s a “fiendishly difficult problem,” says mathematician Kannan Soundararajan of Stanford University, who says he admires Stadlmann’s persistence and courage. “It was really quite impressive.”\n\nWithin three days, an AI startup called Axiom Math had built on Stadlmann’s approaches to best her effort. Within two hours of Axiom’s announcement, both records were surpassed by OpenAI, which just five days later claimed to have solved [another of math’s biggest puzzles](https://www.sciencenews.org/article/ai-math-puzzle-navier-stokes-openai).\n\n“It’s a David-versus-Goliath story where the human gets the gold,” says Kevin Ford, Stadlmann’s postdoctoral mentor at Illinois. For three days, at least.\n\nThe rapid-fire series of events has [sent mathematicians’ angst over AI](https://www.sciencenews.org/article/math-disrupted-by-ai-verify-proofs) skyrocketing. In the view of many researchers, some AI companies are not only subverting professional norms but also undermining researchers’ pursuit of knowledge. “What we are seeing here is a consequence of some very deliberate choices to abandon any pretense of gaining human understanding … and using AI tools for the sole purpose of achieving a benchmark,” Terence Tao of UCLA, a Fields Medalist and probably the most influential blogger in mathematics, [wrote on mathstodon.xyz](https://mathstodon.xyz/@tao/117219548485446992).\n\n## Chasing pairs\n\nPrime numbers, those that can be divided only by one and themselves, are of seemingly endless fascination to mathematicians, who have long puzzled over where along the number line they appear and why. The twin primes conjecture, which has been wrestled with since at least the 19th century, is widely believed to be true but still unproven by number theorists. An easier version of the problem asks not whether there are infinite pairs of primes with a gap of two but whether there are infinite pairs of primes that all have the same gap of any size.\n\nIn 2013, mathematician Yitang Zhang, now at Sun Yat-sen University in Guangzhou, China, proved that answer is yes: Some gaps must repeat infinitely many times. Mathematicians don’t know that a gap of two does, but Zhang showed that a gap of some number less than 70 million does, thus setting the first record for the “small prime-gap bound.”\n\nMathematicians quickly took turns lowering that number. The lower they can push it, the closer they are to solving the twin prime conjecture. By the middle of 2014, massive collaborative efforts had brought the bound down to 246, meaning pairs with some gap size equal to or less than 246 must repeat infinitely. That is where the record stood for a dozen years.\n\nStadlmann began working intensively on the problem about two years ago, after finishing her doctorate under James Maynard at the University of Oxford in England. (Maynard had helped set the previous record, and won the Fields Medal in 2022, in part for his work on prime gaps.) Stadlmann took on the formidable task of trying to better integrate the more recent techniques with Zhang’s earlier efforts.\n\nBoth approaches use a “sieve” method, which partially filters out composite numbers using various weights, for example filtering out multiples of 2 more strongly than multiples of 3. Paradoxically, this idea of partial filtering offers a better idea of the distribution of primes than a complete filter would. Stadlmann determined the optimal weights by piecing together regions of high-dimensional space where the different approaches prevail. She had to calculate the volumes of those regions with only a rough idea of what the regions look like.\n\n“It goes beyond finding a needle in a haystack,” says Andrew Granville, a number theorist at the University of Montreal.\n\nBy early summer 2026, Stadlmann had managed to [move the world record down from 246 to 240](https://arxiv.org/abs/2608.31126). With time, number theorists agree, her methods could have done better. Unfortunately, she did not have time.\n\nIn mid-August, Stadlmann began hearing rumors that OpenAI was planning to announce a big new result on prime gaps. Ford told her: “Drop everything you’re doing and put this result on the math preprint archive. Get it out there. Even if it’s improved the next day, you’ve got the record at least for a day.”\n\nAs it turned out, the record lasted three days. It may be the last time the record will ever be held by a human.\n\nAfter Stadlmann posted her result online, researchers at Axiom Math, who had been checking the proofs published in 2013 and 2014, shifted their energies and incorporated her new ideas into a theorem-proving AI. Over the next three days, pulling all-nighters, researchers at Axiom [got the bound down to 212](https://primegaps.axiommath.ai/bgp212.pdf), a good estimate of what Stadlmann might have achieved with more time and computing resources.\n\nMeanwhile, OpenAI had been working on a closely related problem that asks for the largest gaps between primes instead of the smallest ones. The team had been using it as a benchmark to showcase the problem-solving abilities of its newest large language model, GPT-6 Astra. According to OpenAI computer scientist Sébastien Bubeck, the team was also exploring the small gaps problem, a sort of add-on because mathematicians at the company were interested in it. Astra got the record down to 186, OpenAI reported [in a paper that accompanied the model’s release](https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/short_gaps.pdf) on September 3.\n\nBubeck says that OpenAI does not intend to push their work on the prime-gaps problem further. “Our goal is not to preemptively strike and capture all the results possible,” says Bubeck. “Our strategy is to empower the mathematician.”\n\nBut controversy in the math community swiftly ensued.\n\n## Math for understanding\n\nNo one disputes the idea that AI can be a stunningly useful mathematical tool. “Last week, I did a proof in two hours that would have taken me a month before,” Granville says. AI can sift through the vast literature faster than a human, identify dead ends more quickly, and try many more combinations of ideas.\n\nBut AI also brings many questions: Who will have access to these tools? How much will they cost? What’s the best way to make sense of machine-generated proofs, which can be filled with “AI slop” that humans can’t immediately understand? How will the culture of the field change if a computer can swoop in and make someone’s work immediately obsolete?\n\nThough Stadlmann says she doesn’t feel mistreated, many mathematicians were upset that OpenAI was working on the same problem as Stadlmann without informing her. Typically in mathematics, academics will stand back if others, particularly less senior researchers, are already at work on a problem. Alternatively, they might reach out to collaborate. “I do not see that OpenAI carefully considered how they treated her,” Granville says.\n\nOpenAI says that they were in touch with Maynard, but that they did not contact Stadlmann directly.\n\nMathematicians are now in the process of digesting OpenAI’s paper and the strategy that made the new record possible. “I am not so much interested in the exact number, but I am very interested in the mathematical ideas,” Stadlmann says.\n\nIt’s this pursuit of ideas that mathematicians worry will be lost when AI is let loose on unsolved puzzles. For problems like these, notes Tao, who collaborated on previous small prime-gap efforts, the value is not in the answer, but in what comes out of the struggle. Along the way, mathematicians develop techniques, new ways of thinking about problems and a deeper understanding of mathematics as a whole, which cannot be conveyed by a single number like 186.\n\n“I love the process of problem solving,” Ford says. “Banging our heads against the wall and getting frustrated, and all of a sudden seeing the idea that works.” He worries that as AI takes that away, talented young people will decide not to enter the field. Future researchers may be discouraged from pursuing problems for which a machine can beat them to the answer. “That would be massively detrimental,” he says, “not just to math but to science in general.”", "url": "https://wpnews.pro/news/a-human-set-a-new-mathematical-record-then-ai-came-for-it", "canonical_source": "https://www.sciencenews.org/article/human-math-record-twin-primes-openai", "published_at": "2026-09-11 19:00:00+00:00", "updated_at": "2026-09-11 19:20:45.385123+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "ai-safety", "ai-startups"], "entities": ["Julia Stadlmann", "University of Illinois Urbana–Champaign", "Axiom Math", "OpenAI", "Terence Tao", "Yitang Zhang", "Kannan Soundararajan", "Kevin Ford"], "alternates": {"html": "https://wpnews.pro/news/a-human-set-a-new-mathematical-record-then-ai-came-for-it", "markdown": "https://wpnews.pro/news/a-human-set-a-new-mathematical-record-then-ai-came-for-it.md", "text": "https://wpnews.pro/news/a-human-set-a-new-mathematical-record-then-ai-came-for-it.txt", "jsonld": "https://wpnews.pro/news/a-human-set-a-new-mathematical-record-then-ai-came-for-it.jsonld"}}