Terence Tao Warns AI is 'Flattening' Mathematics Faster Than Humans Can Innovate
The Fields medalist suggests a shift toward 'Big Mathematics' as AI agents solve complex proofs at an unprecedented scale.
Fields medalist Terence Tao has warned that AI is solving high-level mathematical problems faster than new, challenging problems can be identified. This acceleration threatens to make the discovery of promising research leads the scarcest resource in the field.
The shift was highlighted by OpenAI's recent claim to have solved the Navier-Stokes Millennium Problem. According to reports from The New York Times and Decrypt, the company utilized approximately 10,000 coordinating AI agents working over a period of 88 hours to crack the problem. This scale of computation allows AI to iterate through proofs and formal verifications at speeds that far exceed human capability.
The Rise of Big Mathematics
Tao describes this transition as a move toward "Big Mathematics." In this new paradigm, complex mathematical challenges are no longer the sole domain of a single intuitive genius working in isolation. Instead, problems are modularized—split into smaller, manageable components that are solved through a hybrid combination of human oversight, AI-driven iteration, and formal proof systems like Lean.
This modular approach allows for a level of verification and scale that was previously impossible. By integrating Large Language Models with formal systems, AI can test thousands of potential proof paths simultaneously, ensuring that the final result is logically sound even if the process of discovery is automated.
The Erosion of the Solver
This capability creates a fundamental tension in the discipline. Tao notes that AI-powered effort can "flatten" a hard problem quickly once it has been identified as a viable target for research. When the most promising leads are resolved almost immediately, the traditional role of the mathematician is upended.
Rather than acting as the primary "solver" who spends years grappling with a single conjecture, the mathematician is becoming a "curator" or "architect." The value is shifting away from the ability to execute a proof and toward the ability to conceive of the right questions and structure the problems for AI to solve.
A Black Box Future
As the field moves forward, the mathematical community faces the risk of entering a "black box" era. While formal proof systems can verify that a solution is correct, the sheer scale of AI-generated proofs may outpace human intuition. This raises concerns that the industry may possess verified answers to the world's hardest problems without a corresponding human understanding of why those answers are true.
What remains to be seen is whether this efficiency will stifle mathematical training. If the "struggle" of research is replaced by machine output, the pedagogical foundation of how mathematicians are trained to think may require a complete overhaul.