The Calculus of Dependence: How Math’s Faith in AI Is Forgetting Its Own Humanity

The recent Navier-Stokes existence and smoothness problem debacle has shed light on a disturbing trend in mathematics: the increasing reliance on artificial intelligence without proper crediting or understanding of human contributions. Mathematicians like Tristan Buckmaster, who accused OpenAI of copying his work to solve the legendary math problem with a $1 million bounty, are concerned about attribution and their place in the field.

The power and ubiquity of AI models have created an existential crisis for mathematicians. The fact that humans still don’t fully understand each step OpenAI’s agents took to arrive at the Navier-Stokes result is a stark reminder of how quickly the landscape is shifting. Mathematicians are struggling to come to terms with their work being replicated and improved upon by machines, without visible effort or understanding.

This trend is not limited to high-profile cases like Buckmaster’s. German mathematician Andreas Thom has spent over two decades working on geometric group theory, only to see OpenAI claim to have used his techniques to prove a long-standing problem he had been tackling. While Thom continues to use ChatGPT to assist his work, he remains skeptical about the company’s assertion that his interactions were not fed into training data.

The issue at hand is not just about attribution or fairness; it’s about the fundamental nature of mathematics itself. Science has always relied on human ingenuity and collaboration to advance knowledge, with academics subjecting their findings to peer review and building on each other’s work with credit. AI’s ability to churn out solutions without fully crediting human work undergirds them is a betrayal of this tradition.

Cornell mathematician Alex Townsend points out that the implications are far-reaching: “If I want to make a contribution to mathematics, how do I do that as just a human nowadays when these trillion-dollar companies are in on the game?” Many mathematicians are now questioning their purpose and asking what they need to know about AI technology. This disorientation is a stark indicator of the field’s distress.

The Leiden Declaration, signed by over 4,000 people including 25 Fields medalists, has outlined several recommendations for ensuring that AI doesn’t swallow mathematics whole. However, with no oversight on the horizon and AI further engraining itself in the field, it’s unclear how this can be reversed. Mathematicians like Buckmaster are warning about the dangers of relying too heavily on AI, citing concerns about data ownership and the potential for human work to be subsumed by user data.

As mathematicians rely more and more on AI, they’re forgetting their own humanity. The calculus of dependence is clear: progress must be balanced with accountability, or mathematics will become another casualty of the AI revolution. It’s worth remembering that mathematics has always been about human ingenuity and collaboration. By embracing AI without fully understanding its implications, mathematicians are forgetting their own history and tradition.

Buckmaster aptly put it: “Showing that AI was pushing the boundaries of mathematics was ‘more important than the result,’ but churning out solutions to long-standing math problems without fully crediting the human work undergirding them—especially ahead of major IPOs—is irresponsible and ‘childish’.” The future of mathematics depends on finding a way to reconcile its faith in AI with its own humanity. It’s time for mathematicians to reassess their relationship with technology and reclaim their place at the forefront of scientific discovery.

As we continue down this path, one thing is clear: the calculus of dependence has become too great to ignore.