Topic: mathematical research

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.

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.

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.

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.

Terence Tao and Steven Strogatz revisit Tao’s essay on what makes mathematical research valuable. Their conversation examines proof, elegance, usefulness, problem solving, and connections between fields, showing why no single criterion captures all worthwhile mathematics. They also consider how mathematical communities develop judgment and how technological tools affect research.