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.
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34:13
Does Form Really Shape Function?
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.
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47:24
Will We Ever Prove String Theory?
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 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.
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48:39
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.
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46:07
Will AI Ever Understand Language Like Humans?
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.
“The Joy of Why” is a Quanta Magazine podcast about curiosity and the pursuit of knowledge. The mathematician and author Steven Strogatz and the cosmologist and author Janna Levin take turns interviewing leading researchers about the great scientific and mathematical questions of our time. New episodes are released every other Wednesday.Quanta Magazine is a Pulitzer Prize–winning, editorially independent online publication launched and supported by the Simons Foundation to illuminate big ideas in science and math through public service journalism. Quanta’s reporters and editors focus on developments in mathematics, theoretical physics, theoretical computer science and the basic life sciences, emphasizing timely, accurate, in-depth and well-crafted articles for its broad discerning audience. In 2023, Steven Strogatz received a National Academies Eric and Wendy Schmidt Award for Excellence in Science Communications partly for his work on “The Joy of Why.”
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