OpenAI released a list of ten solutions to longstanding mathematical problems that sent the academic community into an immediate uproar. The announcement, titled “10 Advances in Mathematics and Theoretical Computer Science,” included breakthroughs in areas like quantum game theory and sphere packing in higher dimensions. Researchers noted that while a single human solving these would be impressive, a model solving all ten simultaneously would likely be met with disbelief.
The sudden shift in capability
Robert Hart, The Verge’s London-based AI reporter, spoke with several leading mathematicians about the sudden change in the field. The shift occurred over the last six months to a year, compressing five years of slow progress in other industries into a very short period. AI moved from being unable to count the number of R’s in the word “strawberry” to producing work that rivals professional mathematicians.
Models remain terrible at basic arithmetic, days of the week, and time. Hart noted that his boyfriend’s phone assistant still thinks it is Wednesday when it is not. However, the systems have reached a critical mass where they can forge connections between different areas and apply old methods to new problems.
Math is not a single discipline
Mathematics is not a unitary discipline, much like biology. One end involves watching animals and describing behaviour, while the other covers cellular mechanisms and biochemistry. AI is good at some parts but struggles with others. Topology remains an area where mathematicians believe the models are still quite bad, though Hart admits he cannot verify that claim.
The crisis exists in the middle ground. No one fears a mediocre mathematician, but the research element and the cutting edge are where the real questions lie. The fear is whether this will rewrite employment structures or funding models for universities training new generations of humans to identify new problems.
What happened with Astra?
The situation escalated in May with an internal OpenAI model disproving the unit distance conjecture, an 80-year-old problem. Hart suspects this was Astra, though OpenAI listed it only as an unnamed internal model when asked. Recently, the company dropped a blog post along with hundreds of pages of paperwork proving the model’s work.
The solutions were not entirely generated from nothing. They are based on previous work, raising questions of attribution. Some researchers worry that labs have built on the shoulders of giants without mentioning it. By and large, the reaction was one of being impressed, but the lack of attribution remains a point of contention.
What it means for researchers
The core issue is whether frontier models will simply answer all outstanding questions, making academic grants and university programs for training new generations of human mathematicians seem redundant. If a model can solve problems that humans have struggled with for decades, the role of the mathematician shifts from finding the answer to defining the question.
