OpenAI’s unreleased advanced model Astra has solved 10 long-unsolved mathematics problems, according to The Verge, placing AI at the center of a field long treated as one of the highest forms of human reasoning.
Astra tackled 10 open problems
The report said OpenAI published more than 250 pages describing the solutions, along with 60 pages explaining the model’s reasoning. The problems span several difficult areas, including dense sphere packing in high-dimensional spaces tied to data transmission efficiency, limits of error-correcting codes, structural patterns in complex connected networks, quantum game theory, and target search in high-dimensional lattices linked to post-quantum cryptography.
The most closely watched result was a proof for the existence of non-sofic groups. These are infinite mathematical structures that, in broad terms, cannot be approximated by finite ones, and the question had remained unresolved for decades. OpenAI also used the theorem-proving software Lean to verify the solutions and said the problems had seen at least 10 years without progress on their main results, with most of them stagnant for longer.
Credit for the work became the first flashpoint
The breakthrough was followed almost immediately by a dispute over authorship and attribution. Cambridge mathematician Francesco Fournier-Facio and others argued that OpenAI’s initial announcement downplayed recent work by Gábor Kun, Andreas Thom, and others at Hungary’s Alfréd Rényi Institute of Mathematics. Kun’s papers from 2016 and 2019 were described as especially important groundwork.
Kun said he had mixed feelings. He was glad his research had proven useful, while joking that he might become a “very famous unemployed person.” Fournier-Facio was sharper, saying OpenAI chose the version of the story that best fit commercial promotion. In his view, “AI independently solves problems with no progress for a decade” carries far more marketing value than “AI cleverly combines a decade of human ideas,” and that framing risks making human mathematical work look disposable.
After the backlash, OpenAI revised the wording of its announcement. The company changed the claim to say Astra had “solved or made significant progress on long-standing unsolved problems,” and a spokesperson said the revision was meant to reflect prior human research more accurately.
Admiration, shock, and fear inside mathematics
The technical achievement is only one part of the story. James Maynard, a University of Oxford professor and Fields Medal winner, said he had spent the past year doing “soul-searching” about where mathematics is headed. Yang-Hui He of the London Institute for Mathematical Sciences said that, in earlier years, solving any one of these 10 problems could have been enough to help a scholar secure tenure. The pace now has caught the field off guard.
Researchers are also worrying about unequal access. OpenAI estimated that generating the 10 solutions required about $2,000 in API costs, but the actual cost of training and running such systems is far higher, which could leave smaller institutions and underfunded researchers behind. Another concern is commercial pressure on academic judgment. More than 3,400 scholars signed the Leiden Declaration, warning against accepting exaggerated claims from tech companies and cautioning that governments and funders could wrongly conclude that human mathematicians are no longer needed.
Training the next generation is now part of the debate
The educational implications are becoming hard to ignore. Problems of this kind have often served as training grounds for graduate students, helping them build research instinct and technical skill. Maynard said he worries about how to design problems for students that AI still will not be able to solve four years from now.
For younger mathematicians, the pressure is more immediate. The report said many early-career researchers feel “very, very scared” and are starting to question what it means to continue in the field.
Whether AI has originality remains unsettled
Not everyone sees Astra’s performance as proof of full conceptual creativity. Maynard’s initial assessment was that the results are impressive, but not yet at the level of a Fields Medal-class conceptual leap. For now, AI appears to be showing extraordinary strength in combining existing methods rather than introducing deep new concepts or opening entirely new research programs.
Yang-Hui He offered a more optimistic view. He said this could become a turning point for the discipline: wider access to AI may help undergraduates and researchers outside elite institutions produce publishable work, while senior mathematicians hand routine computation over to machines and spend more time on genuinely creative thinking.
Maynard put the uncertainty plainly: “Sometimes it takes time and perspective to realize, ‘there is a genuinely fundamental new idea here.’ But at the current pace, AI may not give mathematicians much time to figure that out.”