Lex Fridman Podcast #472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
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Jun 15, 2025 
Terence Tao, a renowned mathematician and Fields Medal winner, tackles some of the toughest challenges in math and physics. He discusses the Kakeya problem and its complexities, explores the implications of fluid dynamics in understanding turbulence, and highlights the interplay between randomness and structure in mathematics. Tao also delves into the role of AI in mathematical proofs and collaboration, questioning cognitive limits and promoting innovative problem-solving. With his insightful reflections on creativity and technology, this conversation is both enlightening and thought-provoking.
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Navier-Stokes Singularity Challenge
- Navier-Stokes equations describe fluid flow and can unpredictably concentrate energy to create singularities.
- Mathematicians study if singularities, where velocity becomes infinite, can occur despite physical reality never showing them.
Fluid Computation and Blow-Up
- Tao engineered a fluid dynamics equation that blows up by carefully controlling energy transfer between scales.
- This construction suggests Navier-Stokes could simulate a fluid computer performing complex computations, hinting at possible blow-ups.
Emergence in Cellular Automata
- Complex structures emerge in simple cellular automata like Conway's Game of Life with locally applied rules.
- These discrete models share surprising similarities with continuous fluid equations in producing computational phenomena.
