A Somewhat Optimistic View of AI in Mathematics

Summary

In this opinion essay, Robert Wegner considers how AI could change mathematical research while assuming that AI-generated results will generally be checked by trustworthy interactive theorem provers. He distinguishes between a human-in-the-loop future, in which AI combines existing tools and develops theories in obvious directions under human oversight, and a fully superhuman future in which humans have little practical role in doing mathematics. Wegner argues that mathematicians need not fear the second scenario more than people in other intellectual professions, because current frontier systems still appear weak at long-horizon judgment involving many people, resources, or projects. He identifies judgment, intuition, vision, and related abilities as important requirements for removing humans from the loop, while acknowledging that a fully superhuman transition cannot be ruled out. For the more immediate human-in-the-loop scenario, he argues that mathematics derives its core value from its connections to science and other applications, rather than solely from human achievement or understanding. He presents mathematical theories as tools in a network that ultimately points toward applied problems, and suggests that AI could make it practical to investigate difficult, highly detailed problems that mathematicians previously lacked the labor to pursue. He encourages mathematicians to work closer to applications and to collaborate with scientists and engineers, with the long-term goal of combining formally verified mathematics, scientific models, statistics, empirical observations, simulations, and computation. As an illustration, he cites roughly 1,200 Erdős problems, saying humans have solved about 450 and AI has heavily or fully solved about 100 since the end of 2025; he notes that OpenAI’s internal “Astra” model solved three. He speculates that increasingly capable models may solve only about ten additional problems per year as easier problems are exhausted, leaving substantial room for human mathematicians. He concludes that humans may become a smaller part of a much larger mathematical workforce, while the choice of worthwhile problems and the direction of fields remain especially valuable unless AI becomes better than humans at those tasks, which would amount to the fully superhuman scenario.