Number theory has a long history in Manchester, with one of our earliest number theorists being John Littlewood, who spent the years 1908-1911 in Manchester as the Richardson Lecturer in Mathematics.
It was Louis Mordell, who joined Manchester in 1922 as the Fielden chair, that built up a strong number theory group, having attracted such eminent mathematicians as Harold Davenport, Paul Erdős, Kurt Mahler and Beniamino Segre. While in Manchester, Mordell proved his famous theorem concerning the finite generation of the group of rational points on an elliptic curve, and also formulated his most famous conjecture on the finiteness of the set of rational points on curves of higher genus. This conjecture was eventually proved by Gerd Faltings in 1983, for which he was awarded the Fields medal.
It was also at Manchester that Alan Turing invented and implemented the first computer algorithm for finding zeros of the Riemann zeta function. Variants of Turing’s method are still used to this day. More recent number theorists at Manchester include Sir Martin Taylor.
After a brief hiatus, the number theory group has been recently reformed. We now have a very active research group, covering a range of research interests.
- Analytic number theory
- Arithmetic geometry
- Algebraic number theory
- Additive combinatorics
- Distribution of prime numbers
- Rational points
- Unlikely intersections
- Field arithmetic