Tributes paid to Professor Alan Baker

Colleagues have paid tribute to the mathematician and Fellow of Trinity College, Professor Alan Baker (1939-2018), who passed away on 4 February 2018.

Alan Baker, who died after a stroke, was one of the most eminent number theorists in the world. He came to Trinity College from UCL to do a PhD under Harold Davenport; in 1964 he won a Title A Fellowship, later he was appointed a Teaching Fellow, and from 1974 a Professorial Fellow.

In 1970 Professor Baker was awarded a Fields Medal for his fundamental contributions to the theory of Diophantine equations, especially his vast generalization of Gelfond’s method for transcendence proofs. The influence of his theorem on the linear independence of logarithms of algebraic numbers on number theory is hard to overestimate.

Trinity Fellow, Professor Bela Bollobas, said: ‘Alan Baker was only 25 when he obtained a huge generalization of the great theorem of Gelfond and Schneider on transcendental numbers, a result that David Hilbert had expected to be even deeper than the Riemann Hypothesis. As a consequence of his results on transcendental numbers, he gave an effective bound on the size of the solutions of a wide class of diophantine equations, and in some cases could determine all solutions. These were amazing achievements.

His work shows the tremendous value of solving major problems directly, as their solutions often develop into powerful new theories and can influence unexpected areas of mathematics.’

In addition to his brilliant research, Professor Baker wrote several well-regarded books, including Transcendental number theory (1975), A concise introduction to the theory of numbers (1984), Logarithmic forms and Diophantine geometry (with Gisbert Wustholz, 2007), and A comprehensive course in number theory (2012).

Trinity Fellow, Professor Sir Timothy Gowers, said:

‘Alan Baker was a world leader in transcendence theory, a very difficult branch of number theory that aims to prove that certain numbers are not roots of polynomials with integer coefficients. At a young age, he shot to fame by proving a remarkable theorem that established this for a very wide class of numbers and went way beyond what had previously been known. This result was a landmark of twentieth-century mathematics.’