How Did Geometry Create Modern Physics?

The Joy of Why

Steven Strogatz, Janna Levin and Quanta Magazine

Science, Life Sciences

4.9 • 577 Ratings

🗓️ 15 May 2025

⏱️ 46 minutes

🔗️ Recording | iTunes | RSS

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Summary

Geometry is one of the oldest disciplines in human history, yet the worlds it can describe extend far beyond its original use. What began thousands of years ago as a way to measure land and build pyramids was given rigor by Euclid in ancient Greece, became applied to curves and surfaces in the 19th century, and eventually helped Einstein understand the universe.

Yang-Hui He sees geometry as a unifying language for modern physics, a mutual exchange in which each discipline can influence and shape the other. In the latest episode of The Joy of Why, He tells co-host Steven Strogatz how geometry evolved from its practical roots in ancient civilizations to its influence in the theory of general relativity and string theory — and speculates how AI could further revolutionize the field. They also discuss the tension between formal, rigorous mathematics and intuition-driven insight, and why there are two types of mathematicians — “birds” who have a broad overview of ideas from above, and “hedgehogs” who dig deep on one particular idea.

Transcript

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0:00.0	I'm Steve Strogatz, and I'm Janelle Levin, and this is The Joy of Why, a podcast from
0:11.0	Quantum Magazine exploring some of the biggest unanswered questions in math and science today.
0:19.1	Hey, Janma, good to see you. Good to see you.
0:21.6	I wanted to talk to you about something I think you're going to like.
0:24.6	Okay. I'm intrigued already.
0:26.6	Yeah. I think this is right up your alley, geometry.
0:29.6	Oh, nice. Yeah. Everywhere we look, there's geometry.
0:32.6	Well, there is, right? My wife likes to do art, and she was asking me one time, if our room has a seven-foot ceiling and I have an eight-foot canvas and I stick it in the corner, how far out is it going to stick on the floor?
0:47.8	Right. Now, did you really impress her when you came up with a tangent?
0:51.2	Pulling out Pythagoras? Yeah, that's good for a marriage.
0:54.0	Pythagoras did help us that's good for a marriage.
1:10.3	Pythagoras did help us out in our marriage a little bit. Because she did wonder how cumbersome is it going to be. Is this thing going to take up a lot of flow-space? Right, right, exactly. Have you ever seen those paintings that when you look at them nearly edge on, the picture resolves? Yeah, yeah. You see an image of a face. Right.
1:35.7	And so these ideas of like projecting geometries, I mean, I think that's probably in a lot of art practices. Maybe it's not in the forefront of their mind that that's what they're doing, but that is ultimately geometry. Yeah. No, it's all part of our experience as visual beings. Oh, yeah. It's really funny. I think some friends of mine might imagine that we're just talking about triangles, but Einstein replaced the entire theory of gravity with a theory of geometry. It's very sophisticated. The universe is a geometry.
1:39.4	Well, I'm not surprised that you're an easy cell on geometry.
1:40.6	Right, exactly.
1:45.0	But so I recently had a chance to speak with someone who feels the same way. He is a theoretical physicist, Yang Wei He, who loves geometry, and he sees geometry as a kind of unifying language for modern physics.
1:55.0	Hmm. Oh, neat.
1:56.0	I think you're going to enjoy hearing from him.
1:58.0	This is Yang Wei He from London Institute of Mathematical Sciences
2:02.0	and University of Oxford. Awesome. Here we know. Hi, Yang. Really happy to see you here. Pleasure. Great to see you.
2:11.8	Tell me, where are you right now? I'm now at the London Institute for Mathematical Sciences,
2:16.6	which is the rooms that Michael Faraday is to live and work in.
	...

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