Kol Tregaskes3h ago

Terence Tao joins Dwarkesh Patel to explain how Kepler discovered the laws of planetary motion after 20 years of testing random theories and what this reveals about AI progress in science.

- Kepler behaved like a high-temperature LLM generating countless random relationships and geometric ideas over two decades before using Tycho Brahe's precise naked-eye data to derive his three famous laws of ellipses equal areas and the period-distance relation.

Show threadKol Tregaskes3h ago
- Copernicus's simpler heliocentric model with circular orbits actually predicted planetary positions less accurately than Ptolemy's refined geocentric system which had centuries of tweaks.
- Correct theories can initially make worse predictions and survive only through hard-to-articulate human judgment and heuristics that may take decades or centuries to verify.
Show threadKol Tregaskes
- AI has made generating thousands of hypotheses almost free but the real bottleneck is now verification evaluation and separating valuable ideas from massive volumes of slop.
- Small datasets can produce spurious patterns such as Bode's law which seemed to predict missing planets until Neptune's discovery showed it was a numerical coincidence.
9:29pmTypefully
Show threadKol Tregaskes3h ago
- Tao distinguishes artificial cleverness where AI excels at jumping over low walls or solving easy untried problems from true intelligence which builds cumulatively on partial progress through interactive adaptation.
- AI rapidly solved around 50 previously untouched Erdős problems but progress stalled when three teams applied frontier models to the remaining harder challenges.
Show threadKol Tregaskes3h ago
- AI now enriches Tao's papers with far more charts code numerical examples and literature searches making secondary tasks up to five times faster while the deepest deductive core work still happens with pen and paper.
- Human-AI hybrid teams are expected to dominate mathematical discovery for years to come as each supplies complementary strengths of breadth and depth.
Show threadKol Tregaskes3h ago

- Scientists lack a semi-formal language to capture the intuitive heuristics narratives and plausibility judgments they use daily beyond pure logical proofs in systems like Lean.
- Serendipity unplanned interactions and a certain level of distraction remain essential for creativity even as AI automates routine tasks and over-optimisation risks reducing it.

The full episode is available on the usual platforms.

https://x.com/dwarkesh_sp/status/2035446346803777728?s=20

Dwarkesh Patel (@dwarkesh_sp) on X

Terence Tao spent a year at the Institute for Advanced Study - no teaching, no random events of committees, just unlimited time to think. But after a few months, he ran out of ideas. Terence thinks that mathematicians and scientists need a certain level of randomness and

X (formerly Twitter)