GoKawiilMathematician James Maynard has spent a lot of time this past year “soul searching.” A professor at the University of Oxford and winner of the prestigious Fields Medal, Maynard told The Verge he’s been grappling with the future of his field as the traditionally slow-moving discipline hurries to adapt to AI.
Days before we spoke, OpenAI revealed it had produced the solutions to 10 long-standing mathematics problems, some of which had confounded academics for decades. Like generative AI used to produce text and images or propose ideas in science and medicine, the technology learns patterns and connections from the vast amount of material it’s trained on and uses them to create something new. Applied to mathematics, that can mean combining known results, methods, and tools in new ways to attack a problem, sometimes drawing links between disparate fields or resurfacing concepts buried in academic literature.
For Maynard and other mathematicians The Verge spoke to, the announcement has added to a complex swirl of emotions about where their field is headed. There is palpable excitement at the prospect of accelerating mathematical discovery — but also apprehension, and in some cases despair, about what this could mean for the people who have dedicated their lives to the pursuit, and for the generations of future mathematicians who will follow them. Few doubt that a profound upheaval is already underway.
Few doubt that a profound upheaval is already underway.
The problems OpenAI solved, using an advanced unreleased model known as Astra, spanned a wide range of mathematical fields, from the highly abstract to questions with practical implications. One breakthrough concerned how tightly spheres can be packed in more than three dimensions, a problem linked to how efficiently data can be encoded and transmitted. Another pushed the limits of error-correcting codes, which can help recover information from noisy signals. A third resolved two long-standing questions about how complex connected networks can become before structural patterns emerge. Other results on the list tackled problems in quantum game theory and the search for targets inside high-dimensional grids, with implications for techniques used in post-quantum cybersecurity.
One of the most attention-grabbing results concerned the existence of non-sofic groups, infinite mathematical structures that, roughly speaking, cannot be approximated by finite ones. Whether such structures existed at all had remained an open question for decades. It was attention-grabbing for another reason, too: a dispute over how much credit belonged to OpenAI’s AI, and how much to the human mathematicians whose recent work it built upon.
Francesco Fournier-Facio, a mathematician at the University of Cambridge, told The Verge he and others working in that area believed OpenAI’s original announcement minimized the contributions of researchers Andreas Thom and Gábor Kun, whose recent works helped lay the groundwork for the result.
When OpenAI first published its announcement, it said it was sharing “results to problems that have been open and have seen no progress on the main result for at least a decade, and in most cases much longer.” It later changed this to say it was sharing “results, each of which resolves or makes substantial progress on a long-standing open problem.” The page contains no correction note or explanation for the change.
Kun, a researcher at the Alfréd Rényi Institute of Mathematics in Hungary, told The Verge OpenAI reached out to him by email shortly before publishing to share its findings. He found the sweeping language in the original announcement “rather comical,” particularly as the more detailed research paper attached “clearly said that it builds on my results from 2016 and 2019,” the latter coauthored with Thom. “It’s rather sloppy,” Kun said.
“It’s rather sloppy.”
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