‘I’m Really Terrified’: A Mathematician Grapples With AI’s Recent Breakthroughs

Mathematician Steven Strogatz Discusses AI Systems in Recent Mathematical Advances

Mathematician Steven Strogatz of Cornell University has commented on several announcements from AI companies regarding solutions to longstanding mathematical problems. On September 8, 2026, OpenAI stated that it had deployed tens of thousands of AI agents to address the existence and smoothness of solutions to the Navier-Stokes equations, a Millennium Prize problem established by the Clay Mathematics Institute with a $1 million award for a correct solution. The company indicated that its approach built on prior work by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. The result remains subject to independent verification.

Another mathematician, Tristan Buckmaster of New York University, stated that OpenAI became aware of related work he conducted with Levent Alpöge, a researcher at Anthropic, and proceeded with its announcement. Buckmaster has said that OpenAI attempted to shape the attribution of credit for the underlying strategy. These statements have not been independently confirmed by OpenAI.

Strogatz, who is coauthor with Alex Townsend of the forthcoming book *Big Math*, scheduled for release in November 2026, described the sequence of events as part of broader shifts in how mathematical research is conducted. The book examines changes in the relationship between human mathematicians and computational tools.

In the prior week, Anthropic reported that its Claude system had formalized an existing proof of Fermat’s Last Theorem and generated proofs for 29,500 related lemmas. Separate announcements from OpenAI in August 2026 described progress on ten additional open mathematical questions. Strogatz noted that these developments occurred within a short period and that future work at the frontier of certain areas of mathematics would likely require the use of AI systems.

Townsend has applied large language models in his own research. He reported using ChatGPT to assist with a numerical linear algebra problem that had remained unresolved for several decades. Townsend and his coauthors stated that the computational resources and time required for the project would have exceeded practical limits without such assistance. They also indicated that the cost-benefit calculation for pursuing similar problems has changed with the availability of these tools.

Strogatz addressed the specific Navier-Stokes result in an interview. He described the problem as a theoretical question concerning the existence and regularity of solutions to a system of partial differential equations that model fluid motion. He stated that the problem holds limited direct relevance to most practicing engineers in fields such as aerodynamics or civil engineering. He characterized the announcement as a demonstration of system capability directed at a narrow audience of specialists in pure mathematics.

Regarding attribution and the associated prize, Strogatz said he would prefer that Córdoba and Martínez-Zoroa receive recognition if their contribution is determined to be central. He also noted the prior posting by Buckmaster and Alpöge of solutions to three related but distinct cases that are technically simpler than the full Navier-Stokes problem. He observed that Buckmaster has publicly emphasized the contributions of others and described Buckmaster’s conduct as consistent with standard norms of scholarly credit.

Strogatz discussed the continuing role of human mathematicians. He identified the task of explaining machine-generated proofs in terms accessible to other researchers as one area that currently relies on human expertise. He suggested that this explanatory function may persist for a period even as automated systems advance. He further stated that applied mathematics, which involves direct engagement with empirical data and physical constraints, presents greater resistance to full automation than purely formal questions. Disciplines such as economics, sociology, and international relations were cited as areas where similar considerations may apply for some time.

Strogatz also raised the question of how mathematical interest is determined. He noted that the set of true mathematical statements is infinite, while the subset that holds interest for human researchers is smaller. He asked whether automated systems could develop criteria for interest that align with human aesthetic judgments and observed that current systems have not demonstrated such alignment.

On the effects for individual researchers, Townsend stated that the introduction of AI tools has altered his assessment of his position relative to the research frontier. He described a shift from direct production of new results to collaboration with automated systems. Strogatz indicated that the motivation of being the first to resolve a particular question may diminish if automated systems consistently reach solutions ahead of human teams. He compared the situation to competitive chess, where human players continue to participate despite the existence of stronger engines, and to recreational tennis, where participants accept that they will not reach professional levels.

Strogatz noted that funding decisions for human researchers could change if automated systems perform the majority of the work on certain classes of problems. He presented this as one possible outcome rather than a certainty. He also mentioned the possibility that mathematics could retain value as an activity pursued for its intrinsic interest even if professional incentives shift.

Strogatz described mathematics as an initial domain in which the consequences of widespread AI assistance can be observed. He stated that the field offers a setting in which to examine changes in human understanding of technical results, with implications that may later appear in other disciplines. He characterized the current period as one in which the rate of progress on selected open problems has increased, while the distribution of effort between human and automated contributors continues to evolve.

The interview took place in Strogatz’s office at Cornell University, which contains framed certificates of academic recognition. Townsend joined the conversation toward its conclusion. Both researchers emphasized that their statements reflect observations based on the announcements and their direct experience with the tools rather than predictions of specific future events.