Mathematics podcasts

Daniel Litt discusses how he uses AI in mathematical research and why he changed his forecast about automated results. The conversation distinguishes technical proof work and literature coverage from choosing worthwhile questions and developing mathematical understanding. It examines checking machine-generated proofs, the guarantees and limits of Lean formalization, repeated discoveries by different models, and how research assessment might change. Further topics include publication incentives, competition between AI laboratories, teaching mathematics and questions about computational complexity. Statements about the future of mathematics are presented as the guest’s views.

Hosted by Ravid Shwartz Ziv, Allen Roush

Maxim Raginsky joins Paul Middlebrooks to examine brains, AI and biological autonomy through control theory. They discuss what behaviour reveals about a system's internal organisation, analog and digital descriptions, the relationship between control and cybernetics, active inference and the limits of computational accounts. The publisher offers a public episode and supporter access to its full archive.

Hosted by Paul Middlebrooks

Mathematician Maggie Miller of the University of Texas at Austin joins Janna Levin and Steven Strogatz to explore knots, surfaces and four-dimensional topology. They discuss why loops can untangle in four spatial dimensions while two-dimensional surfaces can remain knotted, how three-dimensional snapshots help visualize 4D spaces, and Miller and collaborators’ resolution of a knotted-surface question posed by Charles Livingston in 1982. The conversation also connects visual techniques from art with mathematical reasoning.

Hosted by Janna Levin, Steven Strogatz

Sam Charrington speaks with Greg Burnham, who leads AI capabilities research at Epoch AI, about the progression from elementary mathematical tasks to difficult research problems, including Navier–Stokes. They examine how advanced systems solve mathematical problems, the roles of persistence and existing human work, and the evidence for new ideas. The conversation also considers how to measure progress when traditional benchmarks become less informative, why improvements appear steady across successive model generations, and the remaining weaknesses in open-ended research, learning from experience and choosing productive scientific questions.

Hosted by Sam Charrington

Jonathan Webb and ABC AI reporter Cam Wilson discuss how AI systems are changing mathematical research and the controversy around claims concerning the Navier–Stokes equations and the Millennium Prize. Mathematician Tristan Buckmaster of New York University contributes to the discussion.

Hosted by Jonathan Webb

Leonardo and Andrea discuss internet censorship and recent work on Navier-Stokes equations involving AI, including the scientific significance and debate surrounding the results. The episode also contains Giuliano Greco's interview with Ivano La Rosa about a cyberpunk audio drama set in a future Genoa.

Hosted by Leonardo, Andrea

Mathematicians Sylvia Serfaty and Amaury Hayat discuss AI-assisted mathematical research with Alexandra Delbot. The conversation examines recent claims of difficult problem solving, how researchers assess and understand machine-generated proofs, and the implications for publication, mathematical practice and the responsibilities raised by the Leiden declaration.

Hosted by Alexandra Delbot

Recorded live at the International Congress of Mathematicians in Philadelphia, this episode brings hosts Janna Levin and Steven Strogatz together with Akshay Venkatesh, Ravi Vakil and Alex Kontorovich. They examine what recent AI-generated proofs demonstrate, how machine assistance may change mathematical research, and what proof, creativity, understanding and storytelling contribute to the discipline. The recording took place on 26 July 2026; Quanta published the episode on 3 September 2026.

Hosted by Janna Levin, Steven Strogatz

Ellen Zapata-Webborn discusses how mathematical research can help predict household energy use. The episode connects patterns in smart-meter data, human behaviour and the demands of electricity systems, illustrating how quantitative models can inform practical energy questions.

Gaute Einevoll talks with Tatjana Tchumatchenko about a mechanistic mathematical model of how neurons minimize energy use by deciding whether ion-channel proteins are produced locally in dendrites or in the soma. The model’s predictions agree with experimental findings.

Joe Hilton explains how health economics and mathematical modelling inform difficult decisions about healthcare resources. The conversation contrasts costly treatments benefiting small groups with interventions serving larger populations, and examines how such trade-offs are assessed. Hilton also discusses his route into research and the experience of beginning work on health policy during the COVID-19 pandemic.

Hosted by Rachel Thomas, Marianne Freiberger

Roman Sauer and Uri Bader join Saar and Shaked to discuss a collaborative proof of a rigidity result involving symmetries and group theory. The conversation explores the mathematical result, how family relationships shaped the collaboration, and the participants’ routes into mathematical research at the Isaac Newton Institute.

Hosted by Marianne Freiberger, Rachel Thomas

James Fergusson discusses artificial intelligence and data-intensive science, including how mathematical and computational approaches help researchers learn from complex datasets. The conversation connects research practice with the training needed to work across scientific disciplines.

Holly Krieger discusses arithmetic dynamics: how repeatedly applying simple mathematical rules connects number theory with dynamical systems. The conversation explores the patterns and difficult questions that arise when numbers and iteration meet, providing an accessible route into an active area of mathematical research.

Hannah Fry discusses receiving the 2026 Leelavati Prize, mathematics as part of culture, and her experiences communicating mathematical ideas. The conversation explores why public understanding matters and how sharing mathematical insights can connect research with a wider audience.

Hosted by Marianne Freiberger, Rachel Thomas

Richard Samworth discusses the research behind his invited talk at the 2026 International Congress of Mathematicians. He explains how statistics connects theoretical questions with practical applications and reflects on mathematical collaboration and the research community at Cambridge.

Hosted by Marianne Freiberger, Rachel Thomas

Julian Sahasrabudhe describes his path from childhood ambitions and drumming to mathematical research. He introduces combinatorics and its connections with other areas, including the relationship between Ramsey theory and sphere packing, ahead of his invited lecture at the 2026 International Congress of Mathematicians.

Hosted by Marianne Freiberger, Rachel Thomas

Lauren Williams introduces the positive Grassmannian and the surprising connections it creates across mathematics and physics. She explains links to waves, traffic and particle scattering, and discusses how research-level mathematical problems can help assess what artificial intelligence is capable of proving.

Hosted by Steven Strogatz

Tom Griffiths discusses mathematical accounts of cognition through logic, neural networks and probability. The conversation draws on his book The Laws of Thought to examine how these approaches complement one another, the ideas and people behind them, and prospects for a unified theory of mind.

Taylor Sparks and Oklahoma State University researcher Jake Bair discuss the history and methods of phase-field modelling. They explain how diffuse interfaces represent material transitions and support simulations of crack growth and dendritic structures. The episode links listeners to NIST’s Phase Field Community Hub for further technical resources.

Hosted by Taylor Sparks