Alan Baker (mathematician)

Alan Baker was born in London on 19 August 1939. He attended Stratford Grammar School, East London, and his academic career started as a student of Harold Davenport, at University College London and later at Trinity College, Cambridge, where he received his PhD.[2] He was a visiting scholar at the Institute for Advanced Study in 1970 when he was awarded the Fields Medal at the age of 31.[3] In 1974 he was appointed Professor of Pure Mathematics at Cambridge University, a position he held until 2006 when he became an Emeritus. He was a fellow of Trinity College from 1964 until his death.[2]

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.[4] He has also been made a foreign fellow of the National Academy of Sciences, India.[5]

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.[6] Specifically, Baker showed that if ${\displaystyle \alpha _{1},...,\alpha _{n}}$ are algebraic numbers (besides 0 or 1), and if ${\displaystyle \beta _{1},..,\beta _{n}}$ are irrational algebraic numbers such that the set ${\displaystyle \{1,\beta _{1},...,\beta _{n}\}}$ are linearly independent over the rational numbers, then the number ${\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}}$ is transcendental.

• Baker, Alan (1966), "Linear forms in the logarithms of algebraic numbers. I", Mathematika, 13 (2): 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 (2): 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.[7]
• Baker, Alan; Wüstholz, G. (2007), Logarithmic forms and Diophantine geometry, New Mathematical Monographs, 9, Cambridge University Press, ISBN 978-0-521-88268-2, MR 2382891

• 1970: Fields Medal
• 1972: Adams Prize
• 1973: Fellowship of the Royal Society

• 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
• Masser, David (January 2019). "Alan Baker 1939–2018" (PDF). Notices of the American Mathematical Society. 66 (1): 32–35.