The Calculus of Fear: Mathematicians Confront an Uncertain Future

Mathematicians are grappling with the implications of AI-driven breakthroughs in their field, which have sparked a heated debate about the role of humans in mathematical inquiry. OpenAI’s recent announcement that it had solved a 90-year-old math problem using tens of thousands of agents has left many mathematicians feeling uneasy. Steven Strogatz, a Cornell University professor, candidly admits to being “really terrified” about the rapid changes taking place in his field.

The controversy surrounding this breakthrough highlights the anxiety that is gripping many mathematicians. The issue at hand is not just about who deserves credit for solving a particular problem or whether the solution will lead to significant practical applications. Rather, it’s about what these breakthroughs mean for the future of mathematics as a discipline and its practitioners. Strogatz notes that 2026 may be remembered either as an annus mirabilis (a year of wonders) or annus horribilis (a year of horrors) for mathematics, depending on how the field adapts to the new reality.

The contrast between the excitement generated by AI-driven breakthroughs and the sense of unease among mathematicians is striking. Alex Townsend, a coauthor of Strogatz’s book Big Math, has already been using ChatGPT to accelerate his research and acknowledges that AI has helped him in significant ways. However, he also expresses concern about the changing nature of mathematical work and his own role within it.

“I actually feel kind of upset that I’ve dedicated 15 years of my life to research mathematics,” Townsend says, “and at a point in my career where I’m very productive and at my peak strength as a mathematician, that peak skill is no longer there. Something is able to surpass me.” This sentiment echoes the concerns expressed by other mathematicians who worry about being replaced by machines.

The Navier-Stokes existence and smoothness problem, which was recently solved using AI, is a case in point. Strogatz describes it as a “very theoretical math problem of essentially no interest to a working engineer” and notes that only a small subset of pure mathematicians care about it. However, the solution has significant implications for our understanding of complex systems and may have far-reaching consequences for fields like aerodynamics and civil engineering.

One possible scenario is that human mathematicians will focus on more applied and practical problems that require a deeper understanding of the real world. Strogatz notes that “applied math is messy because it deals with the real world,” and this messiness may be just what makes it resistant to AI. However, even in these areas, there is a risk that machines will eventually surpass human mathematicians.

The current debate among mathematicians highlights the need for a broader conversation about the implications of AI-driven breakthroughs in mathematics. It’s not just about who deserves credit or how to allocate resources; it’s about what these developments mean for the very fabric of mathematical inquiry and its practitioners. As Strogatz so eloquently puts it, “Instinctively, I’m really terrified.” But we would do well to take a step back and consider the implications of this new reality.

What does it mean to be a mathematician in an age where machines are capable of surpassing human intelligence? How will we adapt as a discipline, and what role will human mathematicians play in shaping the future of mathematics? The answers to these questions will not be easy to find, but one thing is clear: the calculus of fear that is gripping many mathematicians today is a symptom of a deeper issue. It’s time for us to confront this uncertainty head-on and to begin building a new understanding of what it means to do mathematics in an age where machines are increasingly capable of doing it better than we can.