Terence Tao – Kepler, Newton, and the true nature of mathematical discovery
3/20/20261 hr 24 min
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.
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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
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Clips
Showing 10 of 12Transcript preview
First 90 secondsDwarkesh Patel· Host0:00
Okay. Today I'm chatting with Terence Tao, who needs no introduction. Terence, I wanna 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.
Terence Tao· Guest0:15
Okay. Yeah. So I've always had an amateur interest in astronomy, and so I've, I've, I've loved stories of how the early astronomers worked out, um, the nature of the universe. Um, so, uh, Kepler was building on the work of Copernicus, um, who was himself building on the work of Aristarchus. Uh, so, uh, Copernicus very famously proposed the heliocentric model that, um, uh, 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, were going around, uh, the Sun. And Copernicus proposed that the orbits of the planets were perfect circles. And his theory kind of fit, uh, the observations that, um, the, the Greeks and the Arabs and the Indians had worked out over, over centuries. Um, I think, uh, Kepler got interested... Uh, he, like he learned about these, these theories, um, in his, in his studies, and he made this observation that the ratios of the, uh, size of the orbits that Copernicus predicted seemed to have some geometric meaning. Um, I think, uh, uh, yeah, he, he started proposing that, uh, you know, if you, if you take, um, say, the orbit of, of, um, say, the Earth and you enclose it in, I think maybe a cube, um, the, uh, the outer sphere of that, that encloses the cube almost matched perfectly the orbit of Mars, and so forth. Um, and there were six planets known at the time, five gaps between them, and there were