#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Lex Fridman Podcast
Jun 15
#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
#472 – Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Lex Fridman Podcast
Jun 15
This podcast features a deep dive into the world of mathematics with Terence Tao, one of the most celebrated mathematicians in history. Known for his groundbreaking work across various mathematical fields, Tao discusses complex problems, the nature of reality, and the evolving role of AI in mathematics.
Terence Tao explores profound mathematical concepts such as the Kakeya problem, Navier-Stokes equations, and infinity's implications in mathematics. He explains how theoretical constructs like the Game of Life illustrate the interplay between randomness and structure. The discussion delves into the relationship between math and physics, emphasizing the challenges of applying abstract concepts to real-world phenomena. Tao also contemplates the pursuit of a theory of everything, unifying general relativity and quantum mechanics, while acknowledging current experimental limitations. He highlights advancements in AI-assisted theorem proving through tools like Lean and DeepMind's AlphaProof, suggesting a future where AI collaborates with mathematicians effectively. The conversation touches on famous conjectures, including the Twin Prime Conjecture, Collatz conjecture, and P = NP, underscoring their complexity and significance. Tao reflects on the impact of prestigious awards like the Fields Medal and shares advice for young people navigating mathematics, advocating for adaptability and lifelong learning. Finally, he muses on influential mathematicians throughout history and expresses optimism about the potential of future generations enhanced by technology.
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Offloading memorization to computers can free the brain for deeper reasoning
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Waves can exhibit both particle and wave behavior, focusing sharply to create singularities.
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Building fluid circuits by constructing complex non-linearities for energy transfer.
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35:31
The Game of Life inspires exploration of Navier-Stokes equations.
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Infinity poses challenges but can be finitized for intuition.
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AI can enhance the experimental component of mathematics
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1:03:08
Mathematicians are categorized as 'foxes' or 'hedgehogs' based on their approach.
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1:22:05
Progress can occur even when starting from incorrect hypotheses.
1:24:45
1:24:45
Imagined being a scalar field to find coordinate change for linear behavior
1:28:31
1:28:31
AI simplifies coding, reducing function-plotting time from hours to minutes.
1:34:30
1:34:30
Formalized proofs make updates easier and parts more readable.
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1:44:48
Equational Theories Project aims to determine which algebraic laws imply others through proofs or counterexamples.
1:54:54
1:54:54
AI performs better on numerical problems due to clear reinforcement learning signals.
1:56:54
1:56:54
AI-generated proofs can seem flawless but often contain subtle and stupid errors.
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2:06:39
By 2026, AI may collaborate with mathematicians on Fields Medal-winning proofs.
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2:19:12
Perelman transformed the problem from super-critical to critical by introducing new quantities.
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2:32:04
The Twin Prime Conjecture tests if primes behave like a random set.
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2:45:46
Statistically, about 90% of inputs would drift down to a much smaller value.
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2:49:50
Solving P = NP positively could solve many other problems.
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2:52:43
Grigori Perelman declined both the Fields Medal and the Millennium Prize.
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3:03:05
Mathematicians value collaboration, tenacity, and fearlessness over secret work.
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3:04:15
Humans don't have an innate math center; they repurpose brain areas for math.
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3:12:43
Mathematicians need to engage in AI and formal proof assistant projects to advance the field.
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3:18:05
Humans are already augmented by technologies like language, and the mathematical community is a super-intelligent entity.
