move the world record down from 246 to 240<\/a>. With time, number theorists agree, her methods could have done better. Unfortunately, she did not have time.<\/p>\nIn mid-August, Stadlmann began hearing rumors that OpenAI was planning to announce a big new result on prime gaps. Ford told her: \u201cDrop everything you\u2019re doing and put this result on the math preprint archive. Get it out there. Even if it\u2019s improved the next day, you\u2019ve got the record at least for a day.\u201d<\/p>\n
As it turned out, the record lasted three days. It may be the last time the record will ever be held by a human.<\/p>\n
After 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, a good estimate of what Stadlmann might have achieved with more time and computing resources.<\/p>\n
Meanwhile, 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 S\u00e9bastien 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\u2019s release on September 3.<\/p>\n
Bubeck says that OpenAI does not intend to push their work on the prime-gaps problem further. \u201cOur goal is not to preemptively strike and capture all the results possible,\u201d says Bubeck. \u201cOur strategy is to empower the mathematician.\u201d<\/p>\n
But controversy in the math community swiftly ensued.<\/p>\n
Math for understanding<\/h2>\n
No one disputes the idea that AI can be a stunningly useful mathematical tool. \u201cLast week, I did a proof in two hours that would have taken me a month before,\u201d 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.<\/p>\n
But AI also brings many questions: Who will have access to these tools? How much will they cost? What\u2019s the best way to make sense of machine-generated proofs, which can be filled with \u201cAI slop\u201d that humans can\u2019t immediately understand? How will the culture of the field change if a computer can swoop in and make someone\u2019s work immediately obsolete?<\/p>\n
Though Stadlmann says she doesn\u2019t 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. \u201cI do not see that OpenAI carefully considered how they treated her,\u201d Granville says.<\/p>\n
OpenAI says that they were in touch with Maynard, but that they did not contact Stadlmann directly.<\/p>\n
Mathematicians are now in the process of digesting OpenAI\u2019s paper and the strategy that made the new record possible. \u201cI am not so much interested in the exact number, but I am very interested in the mathematical ideas,\u201d Stadlmann says.<\/p>\n
It\u2019s 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.<\/p>\n
\u201cI love the process of problem solving,\u201d Ford says. \u201cBanging our heads against the wall and getting frustrated, and all of a sudden seeing the idea that works.\u201d 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. \u201cThat would be massively detrimental,\u201d he says, \u201cnot just to math but to science in general.\u201d<\/p>\n
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