Terence Tao – Kepler, Newton, and the true nature of mathematical discovery

陶哲轩——开普勒、牛顿与数学发现的真谛

Dwarkesh Podcast

2026-03-21

1 小时 23 分钟
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单集简介 ...

We begin the episode with the absolutely ingenious and surprising way in which Kepler discovered the laws of planetary motion. People sometimes say that AI will make especially fast progress at scientific discovery because of tight verification loops. But the story of how we discovered the shape of our solar system shows how the verification loop for correct ideas can be decades (or even millennia) long. During this time, what we know today as the better theory can actually make worse predictions. And the reasons it survives this epistemic hell is some mixture of judgment and heuristics that we don’t even understand well enough to actually articulate, much less codify into an RL loop. Hope you enjoy! Watch on YouTube; read the transcript. Sponsors - Jane Street loves challenging my audience with different creative puzzles. One of my listeners, Shawn, solved Jane Street’s ResNet challenge and posted a great walk-through on X. If you want to try one of these puzzles yourself, there’s one live now at janestreet.com/dwarkesh. - Labelbox can get you rubric-based evals, no matter your domain. These rubrics allow you to give your model feedback on all the dimensions you care about, so you can train how it thinks, not just what it thinks. Whatever you’re focused on—math, physics, finance, psychology or something else—Labelbox can help. Learn more at labelbox.com/dwarkesh. - Mercury just released a new feature called Insights. Insights summarizes your money in and out, showing you your biggest transactions and calling out anything worth paying attention to. It’s a super low-friction way to stay on top of your business. Learn more at mercury.com/insights. Timestamps (00:00:00) – Kepler was a high temperature LLM (00:11:44) – How would we know if there’s a new unifying concept within heaps of AI slop? (00:26:10) – The deductive overhang (00:30:31) – Selection bias in reported AI discoveries (00:46:43) – AI makes papers richer and broader, but not deeper (00:53:00) – If AI solves a problem, can humans get understanding out of it? (00:59:20) – We need a semi-formal language for the way that scientists actually talk to each other (01:09:48) – How Terry uses his time (01:17:05) – Human-AI hybrids will dominate math for a lot longer Get full access to Dwarkesh Podcast at www.dwarkesh.com/subscribe
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  • Okay, today I'm chatting with Terence Tao, who needs an introduction.

  • Terence, I want to begin by having you retell the story of how Kepler discovered the laws of planetary motion,

  • because I think this will be a great jumping off point to talk about AI for math.

  • Okay, yeah.

  • So I've always had an amateur interest in astronomy,

  • and so I've loved stories of how the early astronomers worked out the nature of the universe.

  • So Kepler was building on the work of Copernicus, who was himself. building on the work of Aristarchus.

  • So Copernicus very famously proposed the heliocentric model, that instead of the planets

  • and the sun going around the Earth,

  • that the sun was at the center of the solar system and the other planets were going around the sun.

  • And Copernicus proposed that the orbits of the planets were perfect circles.

  • And his theory kind of fit the observations that the Greeks

  • and the Arabs and the Indians had worked out over centuries.

  • I think Kepler got interested, like he learned about these theories in his studies,

  • and he made this observation that the ratios of the size of the orbits

  • that Kerenko predicted seem to have some geometric meaning.

  • I think he started proposing that, you know,

  • if you take, say, the orbit of, say, the Earth

  • and you enclose it in, I think, maybe a cube, the outer sphere

  • that encloses the cube almost match perfectly the orbit of Mars and so forth.