Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472
Terence Tao talks with Lex Fridman about problem solving, models and reality, mathematical intuition and AI-assisted proofs. He describes Lean as a demanding proof-checking colleague and encourages students to try an approach rather than freeze when stuck. His AI expectations reflect the discussion in June 2025.
Executive Summary (TL;DR)
Tao is drawn to problems on the edge of existing methods, where familiar techniques nearly work but leave an important gap. He separates reality, observations and models, discusses Lean as a strict proof-checking colleague, and sees room for software to expand collaborative experimental mathematics. His advice emphasizes transferable reasoning and trying something when stuck. His AI forecasts are views from the June 2025 discussion.
Key Takeaways
Look near the boundary of what methods can do
Tao distinguishes hard problems from problems that are hopeless with current tools. He finds interest in cases where existing methods do most of the work but leave a remaining gap. This is a way to choose useful research questions, not a claim that the final gap is easy or that any particular percentage can be measured precisely.