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.

Large language models (LLMs) are becoming increasingly more impressive at creating human-like text and answering questions, but whether they can understand the meaning of the words they generate is a hotly debated issue. A big challenge is that LLMs are black boxes; they can make predictions and decisions on the order of words, but they cannot communicate the reasons for doing so.

Ellie Pavlick at Brown University is building models that could help understand how LLMs process language compared with humans. In this episode of The Joy of Why, Pavlick discusses what we know and don’t know about LLM language processing, how their processes differ from humans, and how understanding LLMs better could also help us better appreciate our own capacity for knowledge and creativity.

Quantum gravity is one of the biggest unresolved and challenging problems in physics, as it seeks to reconcile quantum mechanics, which governs the microscopic world, and general relativity, which describes the macroscopic world of gravity and space-time.

Efforts to understand quantum gravity have been focused almost entirely at the theoretical level, but Monika Schleier-Smith at Stanford University has been exploring a novel experimental approach — trying to create quantum gravity from scratch. Using laser-cooled clouds of atoms, she is testing the idea that gravity might be an emergent phenomenon arising from quantum entanglement.

In this episode of the Joy of Why podcast, Schleier-Smith discusses the thinking behind what she admits is a high-risk, high-reward approach, and how her experiments could provide important insights about entanglement and quantum mechanical systems even if the end goal of simulating quantum gravity is never achieved.