AI and the Future of Mathematics with Terry Tao: Navier Stokes, Millennium Problems, and Safety

Video overview

In this New Scientist interview, Terry Tao examines how artificial intelligence is transforming mathematics. AI can quickly solve a wide range of math problems, but Tao argues that math remains fundamentally about understanding, connections, and new ideas. The conversation touches on the Navier Stokes Millennium Problem, AI generated proofs, and the need for responsible practices as capabilities outpace alignment and interpretability.

• AI excels at problem solving but struggles with interpretation and theory formation.
• The Navier Stokes case highlights limits of AI driven proofs and the risk of strip mining fields.
• Mathematics functions as a unifying language across sciences and needs safe integration with AI.
• Future progress requires interdisciplinary collaboration to guide AI in math and education.

AI and the future of mathematics

In this in-depth discussion, New Scientist speaks with Fields Medalist Terry Tao about how artificial intelligence is reshaping mathematical practice. Tao emphasizes that while AI is remarkably capable at solving many mathematics problems, it does not currently deliver the kind of understanding that underpins theory, connections across domains, or the discovery of new ideas. He points to MRI reconstruction and other real-world applications to illustrate how mathematics acts as a bridge between disciplines, a role AI has not yet fully amplified. He argues that AI could be integrated into mathematics in more thoughtful ways than brute force problem solving, requiring new methods to harness its potential without eroding the field’s culture of deep comprehension.

Navier Stokes and the millennium questions

Tao discusses the Navier Stokes problem, one of the seven Millennium Prize Problems, and reflects on the OpenAI claim of solving it using large-scale AI and massive compute. He notes that the published material is AI-generated and not yet understood or accepted in the mathematical community. The proof certificate in Lean verifies correctness, but little mathematical insight has been gleaned from the process. This case raises concerns about how AI might transform research practice, potentially stripping away the gradual, communicative processes by which mathematicians build intuition and future directions. Tao argues for responsible practices that cultivate a field’s health rather than merely achieving an end result.

Models, reality and the limits of abstraction

The conversation shifts to the nature of mathematical models and the limits of abstract thinking. Tao presents a simple framework: there is the real world, the data we observe, and the mathematical models we use to explain it. Models can be accurate in prediction yet fail to capture underlying mechanisms, and vice versa. He uses examples from weather, finance and physics to illustrate the fragility of models when they are treated as exact truths. For Navier Stokes, the mathematical model may predict singularities, but the physical world would be governed by other forces that intervene when reality diverges from the model. This highlights the need for humility and careful domain-specific validation when applying mathematical abstractions to real phenomena.

Three worlds of mathematical thinking and the value of abstraction

Tao discusses abstraction as a safe sandbox in mathematics. He argues that failure is cheap in math, so one can explore toy problems and simplified models before applying methods to the real world. Abstraction allows step-by-step dissection of problems, and the process of building intuition often leads to practical breakthroughs. He shares anecdotes about everyday problem solving and emphasizes that abstraction should ultimately connect back to real-world understanding as part of a broader intellectual journey in mathematics.

Education, six branches and AI as a mathematical problem

The discussion moves to education and Tao’s view of the early, rigorous and post-rigorous phases of mathematical training. He describes six representative branches of mathematics used to illustrate the field’s breadth, noting that logic was considered but ultimately left out in favor of a sampler approach. Tao also contemplates how AI itself may become a focus of mathematical study, given the lack of a complete theory of machine learning. He outlines the mathematical tools needed to understand AI and the gaps that remain in formalizing data complexity, intelligence, and generalization.

Open problems, primes and the parity barrier

The talk ends with Tao’s open problems and his fascination with the twin primes conjecture. He explains how breakthroughs often require new ideas rather than incremental progress, and how parity barriers currently prevent certain goals from being reached. Tao stresses that even the great problems of mathematics are not solved by a single stroke of genius, but by a community of thinkers who develop new concepts that illuminate multiple areas of study. He remains hopeful that mathematics will continue to grow beyond what AI can currently achieve and that collaboration between mathematicians, computer scientists and educators will shape a responsible and productive AI era.

Conclusion

Overall, the interview frames mathematics as a discipline that is deeply human, conceptual, and language-driven while acknowledging that AI can accelerate some aspects of problem solving. Tao calls for careful integration of AI into mathematical practice, robust guardrails for safety, and a broader cross-disciplinary approach to ensure that the future of mathematics remains rich, humane and creative.