Particles of Thought

Jordan Ellenberg tells Hakeem that math isn't just about numbers. It's about everything. The mathematician and bestselling author shares how AI models are trained through trial and error, why geometry secretly governs everything from family trees to statistical correlation, and why uncertainty, not certainty, is the true language of the universe. From new dimensions to hurricanes we can't quite predict, Jordan and Hakeem trace math's fingerprints across physics, language, and daily life in a preview of his upcoming book, Don't Be Too Sure.

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Guest Bio:
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Jordan Ellenberg is a professor of mathematics at the University of Wisconsin–Madison, specializing in number theory and arithmetic algebraic geometry. He is the New York Times bestselling author of How Not to Be Wrong and Shape, and his forthcoming book, Don't Be Too Sure, arrives in 2027

Jordan Ellenberg finds mathematical certainty overrated. Calming our fear of the unknown, the mathematician joins Hakeem to explore why math, contrary to popular belief, is less about proof and more about probability. He traces uncertainty's surprisingly recent arrival in mathematical history and its deep ties to quantum physics. Jordan also unpacks the difference between what's unknown and what's fundamentally unknowable, why hurricanes and earthquakes are "certain u
Learn more about NOVA and visit our YouTube channel.
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Guest Bio:
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin–Madison, specializing in number theory and arithmetic algebraic geometry. He is the New York Times bestselling author of How Not to Be Wrong and Shape, and his forthcoming book, Don't Be Too Sure, arrives in 2027.

Jordan Ellenberg says geometry isn’t about shapes. It’s about distance. In a tour of geometry far stranger than anything from high school, the mathematician breaks down how our ancient understanding of triangles evolved into the invisible architecture behind AI, family trees, and human relationships. Minds expand as we ask why the "closeness" between two ideas is a literal angle in a vast multi-dimensional space, and what can a 19th-century novella about a talking square teach us about worlds we'll never see? 
Learn more about NOVA and visit our YouTube channel.
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Guest Bio:
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin–Madison, specializing in number theory and arithmetic algebraic geometry. He is the New York Times bestselling author of How Not to Be Wrong and Shape, and his forthcoming book, Don't Be Too Sure, arrives in 2027.

Jordan Ellenberg has good news: artificial intelligence is just math you can actually understand. The mathematician joins Hakeem to pull back the curtain on how large language models really work, revealing that the "miracle" of AI is closer to trial and error scaled up billions of times than anything resembling thought. Jordan breaks down why the process works so well, how every word becomes a point in a space with hundreds of dimensions, and why your chatbot's "personality" is engineered, not accidental.

Learn more about NOVA and visit our YouTube channel.
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Guest Bio:
Jordan Ellenberg is a professor of mathematics at the University of Wisconsin–Madison, specializing in number theory and arithmetic algebraic geometry. He is the New York Times bestselling author of How Not to Be Wrong and Shape, and his forthcoming book, Don't Be Too Sure, arrives in 2027.

Ella Al-Shamahi explores what it means to be human. She reveals the surprising truth that our ancestors shared the planet with at least seven other human species as recently as 50,000 years ago. Ella and Hakeem dig into Neanderthal culture and the mysterious Denisovans who were identified from a single finger bone. Then Ella shares something more personal: her own journey from creationist to one of the leading voices in paleoanthropology.
Learn more about NOVA and visit our YouTube channel.
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Guest Bio:
Ella Al-Shamahi is a paleoanthropologist, explorer, and presenter based in London. She specializes in human evolution and has conducted fieldwork in some of the world's most dangerous and remote regions in search of fossil evidence of our earliest ancestors. She is a TED speaker and has appeared in numerous science documentaries, including hosting NOVA and BBC’s five-part series HUMAN, available on the PBS App and NOVA’s website.