The Emotional Impact of AI Advances in Mathematics
Renowned mathematician and author Steven Strogatz expresses profound emotion when discussing the recent advancements driven by artificial intelligence in his field. As a professor at Cornell University, he acknowledges, “Science is exhilarating,” yet he notes that it often presents numerous challenges for individuals involved.
On Tuesday, OpenAI announced a significant breakthrough, having employed tens of thousands of agents to solve a 90-year-old mathematical problem that was linked to a one-million-dollar prize. The solution, which still awaits independent verification, relies on a strategy devised by Spanish mathematicians Diego Córdoba and Luis Martínez-Zoroa. However, the announcement was marred by allegations from fellow mathematician Tristan Buckmaster, who claims that OpenAI rushed to solve the problem after learning of his collaborative work with Anthropic researcher Levent Alpöge. Buckmaster argues that OpenAI also attempted to sway opinions on who would receive credit for the achievement.
This discord exemplifies the rapid transformations occurring in the mathematical realm, spurred by advancements in AI and the competitive race among corporate laboratories to capture headlines before their high-profile IPOs. Last week, Anthropic revealed that its AI system, Claude, had successfully demonstrated 29,500 small theorems while formalising an existing proof of the famed Last Theorem of Fermat — a project that had occupied other mathematicians for years. Strogatz contends that AI is indeed accelerating mathematical progress, but the implications for experts who have devoted their lives to the discipline remain decidedly ambiguous.
The Future of Mathematics in the Age of AI
“I believe 2026 will be remembered as either a year of marvel or horror for mathematics; a great deal has transpired,” Strogatz explains, seated in front of a wall adorned with framed academic diplomas. He adds, “In the future, one cannot hope to compete without AI if they wish to achieve mathematical breakthroughs.”
His co-author, Alex Townsend, has been leveraging this technology to expedite his research for some time. Recently, he utilised ChatGPT to assist in resolving a long-standing numerical linear algebra problem. Towards the conclusion of the interview, Townsend ventures into Strogatz’s attic, reflecting on their shared belief that, without this technology, the workload and cost-benefit relationship would have been prohibitively daunting. Yet, while AI has augmented his work, it has also shifted Townsend’s perspective on the field and his place within it.
“I feel somewhat disheartened having spent 15 years of my life researching mathematics, and now, at a peak moment in my career, when I am most productive as a mathematician, that peak expertise seems diminished,” he confides. “There is now something that can surpass me. It used to be exhilarating to be world-class, to produce excellent research and push the boundaries of knowledge, but now I don’t feel like I am at the forefront of understanding. I am merely an operator of an AI agent, and that feels fundamentally different. I feel entirely threatened by it.”
AI’s Influence on Recognition and the Future of Mathematics
Strogatz likens the current state of mathematics to a horror film, as AI, propelled by systems that are not yet fully understood, looms ever closer. “But we have not yet reached the end of the film,” he remarks. “Instinctively, I am genuinely terrified.”
He reflects on the significance of solving the Navier-Stokes existence and smoothness problem, a highly theoretical conundrum that may hold little interest for civil engineers or aerodynamicists. “This is essentially niche marketing to showcase the quality of their machines. The singularity problem of Navier-Stokes is of concern to only a small group of pure mathematicians. It does not impact anyone else, except that proving superiority over Anthropic could yield a billion-dollar payoff for OpenAI,” he remarks.
When discussing who deserves recognition for solving the problem and claiming the one-million-dollar prize, Strogatz expresses a preference for Córdoba and Martínez-Zoroa to receive the funds, yet he urges caution. “We must also consider Buckmaster and Alpöge; Buckmaster should arguably receive the award, as he and Levent published a couple of days prior to OpenAI’s announcement, addressing closely related Navier-Stokes equations. These are significant problems in their own right, and they were on the right track; it is conceivable they might have succeeded,” he elaborates. “Buckmaster appears meticulous in acknowledging the contributions of others. He is handling the situation with commendable integrity, and it saddens me that he may not obtain the recognition he rightfully deserves.”
The Role of Mathematicians in the Age of AI
Strogatz also ponders whether AI still requires human mathematicians. “We need a profound understanding, meaning we must explain concepts in ways that humans can grasp and appreciate. Currently, the best understanding comes from human experts. Is that where we will remain? Will we become the primary interpreters of what machines accomplish? I suspect we will play that role for some time, retaining that special ability to translate, although I hope machines will soon surpass us in that regard.”
He continues, noting that applied mathematics deals with complex real-world issues. “The more complex the subject matter, the more resistant it is to AI. Thus, disciplines such as economics, international relations, or sociology may remain relatively insulated for the time being,” he suggests. “In mathematics, there are infinite possibilities, yet only a few will capture human interest. Who will arbitrate mathematical taste? Will machines develop an aesthetic sensibility that resonates with us? As of now, they have not demonstrated that capability. However, I see no reason why they could not be trained in aesthetic matters to become proficient in that domain as well.”
The Dual Nature of AI’s Impact on Mathematics
Strogatz concludes that pure mathematics is either being devastated or revolutionised, depending on one’s viewpoint. “Many of the questions we cherish are finding answers, which some of us find unappealing. We love those questions and the challenge of contemplating them. Yet, if one is solely concerned with answers rather than the effort, then satisfaction may be achieved.” He adds, “On the other hand, it is also highly democratizing. Now everyone can engage with mathematics, which is a reasonable argument. I do not wish to be in my ivory tower dismissing this change, especially as a 67-year-old who has dedicated a lifetime to mastering this field. I do not want others to enter without having put in the effort.”
As for the implications for human mathematicians, he warns that the thrill of being the first to conquer a mathematical peak may diminish. “One might ask, ‘Is that the only game in town?’ It is not. I may not play at Wimbledon, but I still enjoy tennis. We may not be as skilled as the top chess programs, yet we still find joy in chess. Could that be the future of mathematics, a beautiful game that we appreciate even if we are not experts? It is a possibility, but it carries significant implications. If mathematics reduces to that, why would anyone fund our pursuits? With AI handling the bulk of the work, there would be little need to invest in human mathematicians, which appears to be a likely trajectory unless we intervene.”
The Broader Implications of AI for Humanity
Strogatz expresses a sense of being on the front lines of a mathematical battlefield, teetering on the brink of losing human comprehension. “Perhaps, fortunately, the consequences may not be dire, but we will see what that means for humanity. Are we the harbingers of what lies ahead for humankind?” he contemplates.