Maths on the Move

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.

Ulrich Sperhake and Seppe Staelens explain hypothetical boson stars and how researchers use mathematical modelling to investigate them. The discussion connects these unusual compact objects to black holes, gravity and gravitational-wave observations.

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

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.

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.

Kevin Buzzard explains how proof assistants check mathematical arguments against axioms and logical rules. The discussion covers the interactive process of formalizing a proof, the collaborative communities around these tools, and the project to formalize Fermat’s Last Theorem. It also examines how proof assistants might work with AI to strengthen mathematical practice.

Moustapha Fall discusses the African Institute for Mathematical Sciences in Senegal, mathematical outreach and challenges facing researchers in sub-Saharan Africa. The conversation considers developing mathematical talent, international scientific collaboration and research integrity, including efforts to address fraudulent publishing.

Hosted by Marianne Freiberger, Rachel Thomas

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.

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.

Zhouli Xu explains the Kervaire invariant problem and the role of unusual geometric objects in high-dimensional topology. He describes the long route towards resolving the problem in dimension 126, including the collaborative and technical challenges behind the proof. The conversation was recorded during the Isaac Newton Institute programme on equivariant homotopy theory.

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.

Adina Goldberg discusses the mathematical study of quantum information and how it differs from classical information encoded in bits. Her perspective on the meaning carried by relationships and arrows connects her research with her career path. The conversation was recorded during a quantum-information research programme at the Isaac Newton Institute.

Recorded during the 2025 Abel Prize celebrations in Oslo, this episode features Masaki Kashiwara on collaboration and creating new mathematics. Ragni Piene offers a perspective on the prize process, and Andrea D’Agnolo reflects on Kashiwara’s role in connecting mathematical fields and the value of long-term research partnerships.

Hosted by Marianne Freiberger, Rachel Thomas

Sarah Hart discusses a career connecting pure mathematics with literature, culture and mathematical history. The conversation ranges from research and public lectures to the mathematics of fictional worlds, exploring how interests beyond a single specialism can inform mathematical communication and a research career.

Hosted by Marianne Freiberger, Rachel Thomas