Computational Mathematics podcasts

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.

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.

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

Carina Hong discusses building systems for mathematical reasoning and machine-verifiable proofs. The conversation explores Lean, the scarcity of formal mathematical training data, and translating natural-language arguments into formal statements. It also examines conjecture-and-proof self-play and applications of formal verification to software and hardware.

Hosted by Sam Charrington

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.

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.

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.

Kevin Buzzard of Imperial College London joins Steven Strogatz to discuss Lean, formal proof assistants and the effort to encode mathematical knowledge in a computer-readable library. They explore how computers verify difficult arguments, the distinction between Lean and its mathematical library, the formalization of work by Peter Scholze and Dustin Clausen, and the prospects and limits of computers creating new mathematics.

Hosted by Steven Strogatz