Interview
Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472
- Mathematics is expected to evolve toward a hybrid model where experimental components, powered by AI, and formalized proofs using tools like Lean become standard, potentially reducing the effort to formalize a proof from 10 times the original writing time to a single-digit multiplier as tooling improves.
- By 2026, collaborations between humans and AI are anticipated to produce published ideas that are at least partially generated or verified by AI, with the possibility of AI systems eventually generating conjectures or proofs significant enough for a Fields Medal.
- Specific mathematical challenges are projected to face distinct trajectories: the Riemann Hypothesis and Twin Prime and Goldbach Conjectures may remain unsolved for extended periods due to parity barriers or the need for unexpected breakthroughs, though partial results for the latter two are expected within the next decade; the Collatz Conjecture may see statistical solutions covering 99% of inputs; and the Navier-Stokes equations may see proofs for global regularity in subcritical/critical cases but potentially finite time blow-up in supercritical cases.
- AI capabilities are predicted to advance toward generating non-trivial conjectures, discovering new laws of physics from data, automatically writing accurate "related work" sections, and eventually verifying proofs with 100% certainty to remove the need for human referees on mechanical correctness.
- The field of mathematics education may shift toward personalized learning styles and diverse cognitive approaches, while research models may transition to crowdsourced projects and "citizen science" involving thousands of contributors working on atomic proof parts.
- Future paradigms may include the unification of general relativity and quantum mechanics, the development of theories describing the universe with fewer than 100 parameters, and a "phase shift" where the distinction between theoretical and experimental mathematics dissolves.
- Potential risks include the "parity barrier" preventing certain number theory proofs, the possibility of the Riemann Hypothesis being disproven causing a shock to cryptography, and career difficulties for researchers obsessing over "mathematical diseases" without sufficient fortitude.
- Long-term outlooks suggest a shift in how prestigious awards are distributed, potentially recognizing human-AI teams or collaborative networks rather than individual genius, alongside the formalization of entire bodies of mathematics down to basic axioms.