Peter Neumann, The Queen's College, Oxford

Galois' Second Memoir
Èvariste Galois died aged twenty, shot in a duel. In spite of the shortness and turbulence of his life he left manuscripts which fundamentally changed the theory of equations and laid the foundations for Modern Algebra. His Second Mémoire, written in 1830, is a difficult and much misunderstood manuscript. Its first part deals with primitive equations that are soluble by radicals, its second with the structure of two-dimensional linear groups over the integers modulo a prime number. In this lecture I shall concentrate only on the first part and focus on three questions---what did Galois mean by `primitive', is his main theorem correct, and how did the notion of primitivity develop in group theory from 1830 to 1870? The lecture will be a mixture of some history of the theory of equations with some fairly modern permutation group theory.