Collingwood Lecture 2026: Professor Don Zagier explores the oldest and newest problems in mathematics

From ancient questions to modern breakthroughs

In his lecture, The oldest and newest, the easiest and hardest maths problems, Professor Zagier guided the audience through the rich and fascinating world of number theory, focusing in particular on Diophantine equations—problems concerned with finding whole number or fractional solutions to polynomial equations. Drawing connections from ancient mathematics to modern research, he explored how some of the simplest-sounding questions have led to profound and far-reaching developments in the field.

The lecture highlighted both historical and contemporary challenges, from problems dating back to Archimedes to celebrated modern breakthroughs such as Fermat’s Last Theorem. Professor Zagier concluded with an accessible discussion of elliptic curves and the Birch and Swinnerton-Dyer conjecture, one of the Clay Millennium Prize Problems, offering the audience insight into one of the deepest open questions in mathematics.

An internationally renowned mathematician

The talk was very well received, reflecting Professor Zagier’s reputation as an engaging and inspiring speaker. A mathematician of exceptional breadth and distinction, he completed his undergraduate studies at the Massachusetts Institute of Technology at the age of 16 and later earned his doctorate from the University of Oxford. Over the course of his career, he has held positions at leading institutions across Europe, the United States, and Asia, and has made fundamental contributions to number theory. His achievements have been recognised with numerous prestigious awards and memberships in national academies.

Engaging with the Durham community

Professor Zagier’s visit to Durham extended beyond the Collingwood Lecture itself. During his time in the department, he delivered a series of additional lectures and took part in a two-day event for early career researchers. He also engaged extensively with postgraduate students and staff through informal discussions, including dedicated sessions and conversations in the department’s communal spaces. These interactions provided valuable opportunities for students and colleagues to exchange ideas and benefit from his insight and experience.

The Collingwood Lecture is a highlight of the department’s annual programme, and this year’s event proved a memorable occasion, showcasing both the enduring appeal and the continuing vitality of mathematical research.