Alan Baker. 19 August 1939—4 February 2018

Abstract

Alan Baker single-handedly transformed several areas of number theory. He achieved a major breakthrough in transcendence and applied it to obtain a new and important large class of transcendental numbers, opening the way to the subsequent discovery of several other such classes. He developed quantitative versions and applied them to the effective solutions of many classical diophantine equations as well as the first effective improvement on the 1844 result by Joseph Liouville (ForMemRS 1850) on diophantine approximation and the resolution of the celebrated Gauss Conjectures of 1801 on class numbers, not only h  = 1 but also h  = 2, of imaginary quadratic fields. He started the study of extensions to elliptic curves, opening the way to later generalizations to abelian varieties and commutative group varieties and in turn their applications to old and new problems in diophantine geometry. In 1970 he was awarded the Fields Medal at the International Congress in Nice on the basis of his outstanding work on linear forms in logarithms and its consequences. He received many other honours, including the prestigious University of Cambridge Adams Prize, and he was made an honorary fellow of University College London, a foreign fellow of the Indian Academy of Science, a foreign fellow of the National Academy of Sciences India, an honorary member of the Hungarian Academy of Sciences and a fellow of the American Mathematical Society.