AI’s takeover of mathematics is already here, with a model not yet released to the public
A few days before the interview, OpenAI disclosed that its advanced model called Astra solved ten open mathematical problems, some of which had seen no progress for decades. The problems span high-dimensional sphere packing (with implications for coding and data transmission), improvement of error-correcting codes, complex networks, quantum game theory, and target search in high-dimensional lattices, a field relevant to post-quantum cryptography. For mathematicians such as James Maynard, professor at Oxford and Fields Medalist, the announcement sparked an “intensive soul-search” about the discipline’s future.
The result that attracted the most attention concerned the existence of non-sofic groups, infinite structures that cannot be approximated by finite ones. The question of whether such groups exist has been open for decades. OpenAI’s original statement claimed that “no progress on the main result for at least a decade”, a phrasing that mathematicians in the field quickly corrected. Francesco Fournier-Facio of Cambridge noted that the announcement disparaged the contributions of Andreas Thom and Gábor Kun, whose recent work laid the groundwork for the proof. Kun, a researcher at the Alfred Rényi Institute in Hungary, described the original wording as “somewhat comical”, especially given that the detailed paper attached to the announcement explicitly acknowledged the prior work. OpenAI later changed the wording to “substantial progress on long-standing open problems”, without attaching a correction note or explanation.
The mathematical community is a mix of excitement and anxiety. On one hand, the prospect of accelerating discoveries at an unprecedented scale; on the other, genuine concern about the role of researchers who have devoted lifetimes to the field, and about a next generation that will grow up in a reality where a model can connect known results, methods and tools in novel ways, sometimes linking distant areas or resurrecting buried concepts. Few doubt that a deep upheaval is already underway.
Astra’s feat is not merely a list of solved problems; it demonstrates the ability to synthesize existing mathematical knowledge at a level approaching the intuition of experts, and sometimes surpassing it. The remaining open question is sociological rather than technical: what will a career in mathematics look like when a model can produce complete proofs for problems that have stood for decades, and what incentive will remain for young researchers to enter a path that has, in part, become automated.