Applied Mathematics podcasts

John Platt discusses how Google’s applied-science team chooses problems where AI can make a useful contribution. Topics include satellite-based detection and prediction of aircraft contrails, evaluation of rerouting trials, limitations of physical simulation, and the role of AI agents in scientific modelling and data work. The conversation also examines overfitting, action incentives, gradient-free optimisation, SMO and support-vector machines, the physical constraints on scaling, and opportunities for robotics and manufacturing to support climate technology. It concludes with FireSat’s approach to detecting small wildfires from orbit and the practical issues of coverage, cost and false positives.

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

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

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.

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

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

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

Steven Niederer and Richard Wilkinson discuss personalised mathematical models of patients’ hearts and their potential use in care. The conversation connects digital twins and the CVDNet project with research on representing, calibrating and using uncertainty in predictions. It also traces how this work develops ideas from the earlier Fickle Heart research programme.

Nicolas Brunel discusses excitation-inhibition balance and mathematical explanations of irregular activity in cortical networks.

Jess Enright, Chris Skinner and Erica Thompson explore role-playing and board-game approaches to understanding mathematical models. Examples connect climate, disease spread and water movement with the limitations of simplified representations. The conversation asks how entering a model’s imagined world can communicate research and help researchers reflect on what their assumptions include or leave out.

Codina Cotar discusses mathematical patterns associated with stochastic systems and anomalous diffusion, using entries in a science-and-art competition to explain the ideas. The conversation connects diffusion with familiar materials, quantum phenomena, movement and visual art, and examines how mathematical models inspire creative interpretations of nature.

Michael Hill explains how topological data analysis extracts structural information from large datasets. Ideas about connectedness, holes and shape, traditionally associated with pure mathematics, provide tools for recognising patterns as the scale of analysis changes. The discussion explores applications including breast-cancer research and questions about fair voting.

Michael Breakspear and Mac Shine examine how neural dynamics change from individual cells to whole-brain systems. Their work connects gain modulation with the balance between integration and segregation, relates it to arousal pathways, and uses coarse-graining to investigate both scale-dependent coding and shared dynamical properties across neural populations.

Hosted by Paul Middlebrooks

Xaq Pitkow describes a principles-based approach to explaining cognition. Topics include inverse rational control, strategies that are rational relative to an organism’s beliefs, probabilistic computation and graph-network inference. The conversation also considers attention, constraints on neural codes and studying cognition in ecological settings.

Hosted by Paul Middlebrooks

Liz Fearon describes a project that involves members of the public as equal participants in creating mathematical models. The discussion asks how models used in public-health policy and other decisions can reflect lived experience, social interactions and community priorities. It explores the motivation, working methods and aims of co-production in epidemiological modelling.

Yolanne Lee, Georg Maierhofer and Chris Budd report on a two-day Maths4DL hackathon investigating machine-learning methods for differential equations. They discuss how such systems can be taught to solve equations, how proposed methods should be evaluated, and the collaborative process of moving from an ambitious research question to workable tests.

Eirik Valseth discusses mathematical models of weather and storm surges and the computations used to make forecasts. Conversation in Norwegian.

Chris Budd describes conversations between AI researchers and UK parliamentarians during Evidence Week. The episode examines algorithmic bias, potential medical applications and the mathematical foundations needed to understand AI. It considers how communication between researchers and policymakers, together with stronger mathematics education, can inform decisions about the technology.

Gaute Einevoll reflects on his academic career and explains his research in mathematical neuroscience, brain physics and neurotechnology. Anniversary solo episode in Norwegian.

Benjamin Walker, Adam Townsend and Andrew Krause explain VisualPDE, an interactive tool for solving and exploring partial differential equations. Examples include airborne infection and flood-water movement. The conversation covers why the tool was built, how interactive simulations make models understandable to non-specialists, and how researchers can quickly investigate the behaviour of their equations.