How Did Geometry Create Modern Physics?

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.