Alan Baker (mathematician)

For other people with the same name, see Alan Baker.

Alan Baker FRS
JET Photographic
Born	(1939-08-19)19 August 1939 London, England
Died	4 February 2018(2018-02-04) (aged 78) Cambridge, England
Nationality	British
Alma mater	University College London University of Cambridge
Known for	Number theory Diophantine equations Baker's theorem
Awards	Fields Medal (1970) Adams Prize (1972)
Scientific career
Fields	Mathematics
Institutions	Institute for Advanced Study, Princeton University of Cambridge
Thesis	Some Aspects of Diophantine Approximation  (1964)
Doctoral advisor	Harold Davenport
Doctoral students	John Coates Yuval Flicker Roger Heath-Brown David Masser Cameron Stewart

Alan Baker FRS (19 August 1939 – 4 February 2018) was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.

Life

Alan Baker was born in London on 19 August 1939. He was awarded the Fields Medal in 1970, at age 31. His academic career started as a student of Harold Davenport, at University College London and later at Cambridge, where he received his PhD. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970. He was a fellow of Trinity College, Cambridge.

His interests were in number theory, transcendence, logarithmic forms, effective methods, Diophantine geometry and Diophantine analysis.

In 2012 he became a fellow of the American Mathematical Society.

Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem. Specifically, Baker showed that if $\alpha _{1},...,\alpha _{n}$ are algebraic numbers (besides 0 or 1), and if $\beta _{1},..,\beta _{n}$ are irrational algebraic numbers such that the set $\{1,\beta _{1},...,\beta _{n}\}$ are linearly independent over the rational numbers, then the number $\alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}$ is transcendental.

Selected publications

• Baker, Alan (1966), "Linear forms in the logarithms of algebraic numbers. I", Mathematika, 13: 204–216, doi:10.1112/S0025579300003971, ISSN 0025-5793, MR 0220680
• Baker, Alan (1967a), "Linear forms in the logarithms of algebraic numbers. II", Mathematika, 14: 102–107, doi:10.1112/S0025579300008068, ISSN 0025-5793, MR 0220680
• Baker, Alan (1967b), "Linear forms in the logarithms of algebraic numbers. III", Mathematika, 14: 220–228, doi:10.1112/S0025579300003843, ISSN 0025-5793, MR 0220680
• Baker, Alan (1990), Transcendental number theory, Cambridge Mathematical Library (2nd ed.), Cambridge University Press, ISBN 978-0-521-39791-9, MR 0422171; 1st edition. 1975.
• Baker, Alan; Wüstholz, G. (2007), Logarithmic forms and Diophantine geometry, New Mathematical Monographs, vol. 9, Cambridge University Press, ISBN 978-0-521-88268-2, MR 2382891

Honours and awards

• 1970: Fields Medal
• 1972: Adams Prize

External links

• O'Connor, John J.; Robertson, Edmund F., "Alan Baker", MacTutor History of Mathematics Archive, University of St Andrews
• Alan Baker at the Mathematics Genealogy Project