Arithmetic Geometry and Computation
Professor of Mathematics
Minhyong Kim explores the interface of arithmetic geometry and computation, tracing the evolution of solving Diophantine equations from antiquity to the profound implications of Faltings' theorem.
In this 2026 Abel Prize Lecture, Professor Minhyong Kim (International Centre for Mathematical Sciences, Edinburgh @ICMS-Edinburgh) asks how far mathematics can go in actually computing the solutions to equations — and where Gerd Faltings' work marks the boundary of what is possible.
Titled "Arithmetic Geometry and Computation," this lecture provides an elegant bridge between historical mathematical problems and cutting-edge research. Kim traces how the ancient search for whole-number solutions, from Diophantus and Fermat onward, leads through elliptic curves, Mordell's conjecture, settled by Faltings and now known as Faltings' theorem, and the Birch-Swinnerton-Dyer conjecture, before turning to a provocative modern question: can the rational solutions of an equation ever be found by an algorithm, and what might artificial intelligence mean for the future of mathematical proof?
Seminar notes & discussion
No public seminar notes on this lecture yet.