Terence Tao – Kepler, Newton, and the true nature of mathematical discovery
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Okay. Today, I'm chatting with Terence Tao, who needs some 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.
Okay. Yeah. So I've always had amateur interest in astronomy, and so I've I've 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 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 fits, th
The take I wanna try on you Mhmm. Is that Kepler was a high temperature LLM, where Newton comes up with this, explanation of why the three laws of planetary motion must be true. And, of course, the way that Kepler discovers the laws of planetary motion or figures out the relative orbits of the different planets is, as you say, a work of genius. But then, you know, he's through his career, he's just trying random relationships. And in fact, the in the book in which he writes down the third law of planetary motion, it's sort of an aside on the harmonics of the world, which is this book about, yo
Mhmm.
And so Newton works that out. But the reason I, I think this is an interesting story is I feel like LLMs can do the kind of thing of, like, twenty years. Let's try random relationships, some of which make no sense. As long as there's a verifiable data bank, like Brahi's dataset
Mhmm.
Where, okay, I'm gonna try out random things about like musical notes. I'm gonna try out random things about platonic objects. I'm gonna All these different geometries. I have this bias that there's some important thing about the geometry of these orbits. And then one thing works. And as long as you can verify it, it can then draw These empirical regularities can then drive actual deep scientific progress.
Traditionally, when we talk about the history of science, idea generation has always been kind of the prestige part of science. So, I mean, a scientific problem comes with there's many steps. You know? You you have to identify a problem, and then you have to identify a good problem to work on, a fruitful problem. And then you need to to collect data. You need to figure out a strategy to analyze the data, to make a hypothesis. And at this at this point, you need to propose a good hypothesis, and then you need to validate. Yeah. So this and then you need to write things up and explain. There's t
Oh, interesting. I I I actually feel like the mold of twentieth century science that you're describing is actually very well described with Habermann and Kepler, where he did have these ideas. 1595 and '96 is where he comes up with first polygons and then, platonic objects theory, but they were wrong. And then a few years later, he gets brought his data. And it's only after twenty years of just trying random things that he gets this empirical regularity. And so it actually feels a bit closer to Brahe's data is analogous to some massive data vanco simulations. And then we he now he now that you
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