Particles of Thought

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.--------------------------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.--------------------------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.--------------------------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.

Ella Al-Shamahi set out to disprove the theory of evolution. Now she’s one of its greatest advocates. In this deeply personal conversation, Ella tells Hakeem her story. She started university as an avid creationist missionary with the intention of disproving evolution, and then her world started to fall apart. This candid conversation covers what the journey from creationist to paleoanthropologist actually looked like, and the evidence that shifted her thinking. It is a path with personal costs and the impact of changing worldviews. It's a thoughtful reflection on science, identity, community and why empathy matters more than argument when deeply held beliefs meet new evidence. Learn more about NOVA and visit our YouTube channel.--------------------------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.

Ella Al-Shamahi thinks Neanderthals have a reputation problem, and the science backs her up. For decades, the word "Neanderthal" has been shorthand for something primitive and brutish. But the archaeological record tells a more nuanced story. Ella joins Hakeem to explore what we actually know about our closest ancient relatives: how they looked, how they lived, what their culture reveals about their inner lives, and if we would even recognize one walking around today. They also dig into the remarkable story of the Denisovans, a species shrouded in mystery and identified first not from a skull or skeleton, but from a single finger bone. Learn more about NOVA and visit our YouTube channel.--------------------------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.

Ella Al-Shamahi says the iconic picture of human evolution is all wrong. She joins Hakeem to take apart the conventional image of the straight-line march of evolution from ape to modern human. The fossil and DNA record tells a far more complex story. As recently as 50,000 years ago, our ancestors shared the planet with at least seven other human species. From the small-statured Hobbits of Indonesia to the mysterious Denisovans of East Asia, the world was very different, and new research suggests that roughly 20% of our genome may trace back to an unknown “ghost lineage” of human species. Human evolution wasn't a straight line, it was a sprawling, interconnected web. Learn more about NOVA and visit our YouTube channel.--------------------------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.

Daniela Rus brings robots and AI together, and as a computer scientist and roboticist at MIT, she's here to set the record straight. She's not just studying AI from the outside. She's building it, and finding ways to make everyday life better. Daniela joins Hakeem to pull back the curtain on what AI actually is, how it really works, and where it is genuinely headed. What happens when AI leaves the cloud and moves into your phone, your car, and even your body? And what does a tiny worm with 302 neurons have to do with the future of machine intelligence? From the history of AI to so-called “liquid networks,” self-driving cars, humanoid robots, and an origami surgeon you can swallow, this conversation covers the full scope of what MIT's most ambitious minds are building right now.Learn more about NOVA and visit our YouTube channel.Daniela Rus is a computer scientist and roboticist at MIT, where she serves as Director of the Computer Science and Artificial Intelligence Laboratory (CSAIL). Her research focuses on the science and engineering of autonomy, including the development of new AI models, and physically intelligent systems. She is the co-founder of Liquid AI, a startup bringing energy-efficient on-device AI models to real-world applications.

Daniela Rus is cutting through the AI hype and headlines to give us a real understanding of its future. As Director of MIT's Computer Science and Artificial Intelligence Laboratory, she has a front-row seat to what AI actually is, how it actually works, and what it can and cannot do. Daniela joins Hakeem to map out the full landscape of a field that is far richer than chatbots and large language models. What are the different types of AI we have today, and how does each one work? Why did methods invented 40 years ago suddenly start working? And how does Daniela envision the impact of AI on the job landscape of the future?Learn more about NOVA and visit our YouTube channel.--------------------------Guest Bio:Daniela Rus is a computer scientist and roboticist at MIT, where she serves as Director of the Computer Science and Artificial Intelligence Laboratory (CSAIL). Her research focuses on the science and engineering of autonomy, including the development of new AI models,, and physically intelligent systems. She is the co-founder of Liquid AI, a startup bringing energy-efficient on-device AI models to real-world applications.

Daniela Rus has built a robot you can swallow, and that is one of the less surprising things her lab is working on. At MIT's CSAIL, she is leading research at the frontier where artificial intelligence meets the physical world, and the results are unlike anything people have imagined. Daniela joins Hakeem to explore what it will really take for machines to move, reason, and interact the way humans do. Why are today's humanoid robots mechanically impressive but intellectually limited? What is the difference between physical AI and embodied intelligence, and why does it matter? From origami surgeons, to robots inspired by the octopus, this is a conversation about the machines of the futureLearn more about NOVA and visit our YouTube channel.--------------------------Guest Bio:Daniela Rus is a computer scientist and roboticist at MIT, where she serves as Director of the Computer Science and Artificial Intelligence Laboratory (CSAIL). Her research focuses on the science and engineering of autonomy, including the development of new AI models, and physically intelligent systems. She is the co-founder of Liquid AI, a startup bringing energy-efficient on-device AI models to real-world applications.

Daniela Rus wants to put AI in your pocket, your car, and your dishwasher. In fact, she has already started. As one of the world's leading AI and robotics researchers, she is building a future where artificial intelligence doesn't live in a distant data center but runs quietly and efficiently on the devices around you. The key is liquid networks, AI models inspired by a tiny worm that gets by on just 302 neurons and that are up to 1,000 times more energy efficient than traditional approaches. Daniela joins Hakeem to explore what that shift actually means: for self-driving vehicles, for privacy, for security, and for the possibility that everyone could soon have offline access to powerful AI. Learn more about NOVA and visit our YouTube channel.--------------------------Guest Bio:Daniela Rus is a computer scientist and roboticist at MIT, where she serves as Director of the Computer Science and Artificial Intelligence Laboratory (CSAIL). Her research focuses on the science and engineering of autonomy, including the development of new AI models, and physically intelligent systems. She is the co-founder of Liquid AI, a startup bringing energy-efficient on-device AI models to real-world applications.