Dwarkesh Patel

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.

take I want to try on you 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, through his career, he's just trying random relationships.

And in fact, 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, you know, all these different planets have these different harmonies.

And the reason there's so much famine and misery on Earth is because the Earth is mi fa mi.

That's the note of Earth.

And so all this random astrology.

But in there is the cube square law, which tells you what relationship the...

The period has to a planet's distance from the Sun which is as you're detailing if you add that to Newton's F equals ma and then the equation for centripetal acceleration You get the inverse square law and so Newton works that out.

But the reason I am I think this is an interesting story is

is I feel like LLMs can do the kind of thing of like 20 years let's try random relationships some of which make no sense as long as there's a verifiable data bank like Brahe's data set where okay I'm going to try out random things about like musical notes I'm going to try out random things about platonic objects I'm going to 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 drive, these empirical regularities can then drive actual deep scientific progress.

Oh, interesting.

I actually feel like the mold of 20th century science that you're describing is actually very well describes what happened in 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.