AI in mathematics is solving some of the field’s best problems faster than new ones are being discovered. Terence Tao, a UCLA professor widely considered the best living pure mathematician and a 2006 Fields Medal recipient, warned on Mathstodon that AI is draining the field’s supply of good open problems. Labs have put models to the test on problems in math, physics, and medicine, and in May an OpenAI model disproved the Erdős unit-distance conjecture.
Terence Tao is a UCLA professor widely regarded as the best living pure mathematician and was awarded the Fields Medal in 2006. On Mathstodon, Tao warned that AI is draining the mathematical field’s supply of good open problems, reducing the set of challenges available to researchers. He identified powerful solution-extraction tools and cautioned that their indiscriminate use can achieve immediate short-term problem solving while coming at the cost of sustaining the ecosystem for the next wave of progress. He also warned that this practice may impede understanding of progress already obtained. These statements together summarize Tao’s public concern about the long-term effects of AI on the mathematical research ecosystem broadly.
AI labs have put models to the test on challenging problems in mathematics, physics, and medicine. In May, an OpenAI model disproved the Erdős unit-distance conjecture. The Erdős unit-distance conjecture concerns how many pairs of points on a plane can sit exactly one unit apart. These tests have included a range of problems from quantum physics to applied mathematics and medicine.
Anthropic researcher Levent Alpöge ran the identical unit-distance problem through Claude Mythos, the company’s unreleased top-tier model, offline so it could not copy OpenAI’s published solution. Anthropic engineer Sholto Douglas described Mythos’s result as a ‘cute, simple proof’ and said it was shorter than OpenAI’s. Mathematician Daniel Litt assessed Mythos’s proof as ‘a bit worse’ than OpenAI’s version, though Mythos also identified OpenAI’s solution. These comparative assessments accompanied the broader testing of models on hard scientific problems.
AI labs have put models to the test on challenging problems across mathematics, physics, and medicine. In May, an OpenAI model disproved the Erdős unit-distance conjecture, which concerns how many pairs of points on a plane can sit exactly one unit apart. Reported results from these model tests have ranged from quantum physics to applied mathematics and medicine. These tests have been carried out by multiple laboratories.
The rapid pace of AI-driven problem solving has prompted concerns about sustaining the mathematical research ecosystem for future progress. The material links these concerns to the indiscriminate use of powerful solution-extraction tools and the potential cost to long-term understanding and development. The content also references frontier AI systems and reasoning models in relation to these developments. Comparative assessments of AI-generated proofs and solutions have been reported among researchers and engineers.
The developments have raised questions about the future supply of open problems in mathematics. The reported results span multiple scientific domains.
AI in mathematics has recently produced solutions to prominent problems and has been tested on challenges in related scientific fields. This rapid problem solving has prompted warnings from leading mathematicians, including Terence Tao, that it could reduce the supply of good open problems and strain the research ecosystem. Observers have linked these developments to the use of powerful frontier AI systems and reasoning models and to broader impacts across disciplines such as physics and medicine.
