On September 8, 2026, OpenAI revealed that it had produced an AI-generated answer to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. This announcement ignited debate within the mathematical community regarding the attribution of credit between humans and machines, as well as the broader implications of AI tackling complex intellectual challenges traditionally seen as uniquely human.
Some mathematicians likened the event to the historic Deep Blue victory over Kasparov in chess, raising questions about whether mathematics itself might be "solved" by AI, similar to how AI has mastered games like chess and Go. However, experts caution against viewing mathematics purely as a game with definitive winners.
Philosophers and mathematicians emphasize that mathematics encompasses more than problem-solving. It involves developing new theories, fostering understanding, building scholarly communities, and appreciating the aesthetic dimensions of the discipline. The recent AI achievement challenges the assumption that providing an answer equates to solving a mathematical problem.
OpenAI’s contribution includes a Lean formalization—a mechanically verifiable proof—and an accompanying manuscript that appears to present an informal proof. While this satisfies the logical notion of proof, which demands formal correctness, it falls short of the intelligible notion of proof valued by mathematicians. The latter requires explanations that humans can comprehend, communicate, and build upon to advance mathematical knowledge.
Historically, logical and intelligible proofs have been intertwined, but AI-generated proofs risk separating these aspects, producing formally correct results that lack human-understandable insight. Genuine mathematical solutions require both formal validity and intelligibility to be truly valuable.
Moreover, even if future AI systems generate proofs that meet both criteria, it would be misleading to say mathematics has been "solved." Unlike games with clear victory conditions, mathematics is an open-ended, collaborative endeavor without a final endpoint. AI is better viewed as a tool to assist mathematicians rather than a competitor.
The mathematical community is now reflecting on its values and practices, especially concerning the emphasis on problem-solving and credit allocation. There is concern that equating mathematical success solely with producing certified answers could narrow the discipline’s scope and diminish its humanistic aspects.
Ultimately, AI’s integration into mathematics presents an opportunity to reconsider what the field aims to achieve. The focus should shift from competition with machines to leveraging AI as a technology that supports and enriches the diverse goals of mathematical practice.