How did geometry create modern physics?

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. Listen on Apple Podcasts, Spotify, TuneIn or your favorite podcasting app, or you can stream it from Quanta. All episodes Your browser does not support the audio element. Transcript [Music plays] STEVE STROGATZ: I’m Steve Strogatz JANNA LEVIN: And I am Janna Levin STROGATZ: And this is The Joy of Why, a podcast from Quanta Magazine exploring some of the biggest unanswered questions in math and science today. LEVIN: Hey! STROGATZ: Hey, Janna. Good to see you. LEVIN: Good to see you. STROGATZ: I wanted to talk to you about something I think you’re going to like. LEVIN: Okay, I’m intrigued already. STROGATZ: Yeah, I think this is right up your alley: Geometry. LEVIN: Oh, nice. Yeah, everywhere we look there’s geometry. STROGATZ: 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 f...