In this episode of the Lex Fridman Podcast, Lex interviews Terence Tao, a highly regarded mathematician, discussing a range of complex mathematical concepts and problems. Tao explains the Kakeya problem and its connections to various fields, delves into the Navier-Stokes equations and the possibility of finite time blow-up, and explores the idea of constructing a liquid computer to solve fluid dynamics problems. They discuss the dichotomy between structure and randomness in mathematics, the challenges of working with infinity, and the differences between mathematics, physics, and engineering. The conversation also covers the potential of AI in mathematics, the nature of mathematical beauty, and the importance of collaboration and diverse thinking styles in solving difficult problems, with Tao sharing personal anecdotes and insights into his problem-solving approach.
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