Born in the 18th century when Leonhard Euler solved the puzzle of the seven bridges of Königsberg, graph theory has become a foundational tool in mathematics. It studies relationships through nodes (vertices) and the links (edges) that connect them, transforming the complexity of systems — from friendship networks to airline routes — into elegant abstractions that reveal underlying structure and interaction.

Maria Chudnovsky from Princeton University is a leading mathematician in the field. In this episode of The Joy of Why, Chudnovsky talks with co-host Janna Levin about how she got into graph theory, solved the decades-old perfect graph problem, and used it to plan her wedding seating chart. Chudnovsky also reflects on her appearance in commercials as a “superstar mathematician,” and how her background primed her for a discipline that transcends language, culture and time.

What links a Möbius strip, brain folds and termite mounds? The answer is Harvard University’s L. Mahadevan, whose career has been devoted to using mathematics and physics to explore the form and function of common phenomena.

Mahadevan, or Maha to his friends and colleagues, has long been fascinated by questions one wouldn’t normally ask — from the equilibrium shape of inert objects like a Möbius strip, to the complex factors that drive biological systems like morphogenesis or social insect colonies.

In this episode of The Joy of Why, Mahadevan tells co-host Steven Strogatz what inspires him to tackle these questions, and how gels, gypsum and LED lights can help uncover form and function in biological systems. He also offers some provocative thoughts about how noisy random processes might underlie our intuitions about geometry.

For decades, string theory has been hailed as the leading candidate for the theory of everything in our universe. Yet despite its mathematical elegance, the theory still lacks empirical evidence.

One of its most intriguing, yet vexing, implications is that if all matter and forces are composed of vibrations of tiny strands of energy, then this allows for a vast landscape of possible universes with different physical properties, varieties of particles and complex spacetimes. How, then, can we possibly pinpoint our own universe within a field of almost infinite possibilities?

Since 2005, Cumrun Vafa(opens a new tab) at MIT has been working to weed out this crowded landscape by identifying which hypothetical universes lie in a ‘swampland’ with properties inconsistent with the world we observe. In this episode of The Joy of Why, Vafa talks to co-host Janna Levin about the current state of string theory, why there are no more than 11 dimensions, how his swampland concept got an unexpected lift from the BICEP array, and how close we may be to testable predictions.