Alan Baker (mathematician)
19 August 1939|
4 February 2018 (aged 78)|
University College London|
University of Cambridge
Fields Medal (1970)|
Adams Prize (1972)
|Institutions||University of Cambridge|
|Thesis||Some Aspects of Diophantine Approximation (1964)|
|Doctoral advisor||Harold Davenport|
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.
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.
Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem. Specifically, Baker showed that if are algebraic numbers (besides 0 or 1), and if are irrational algebraic numbers such that the set are linearly independent over the rational numbers, then the number is transcendental.
- 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, 9, Cambridge University Press, ISBN 978-0-521-88268-2, MR 2382891
Honours and awards
- Trinity College website, accessed 5 February 2018
- Institute for Advanced Study: A Community of Scholars Archived 6 January 2013 at the Wayback Machine.
- List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
- "National Academy of Sciences, India: Foreign Fellows". Retrieved 2 June 2018.
- Biography in Encyclopædia Britannica. http://www.britannica.com/eb/article-9084909/Alan-Baker
- Stolarsky, Kenneth B. (1978). "Review: Transcendental number theory by Alan Baker; Lectures on transcendental numbers by Kurt Mahler; Nombres transcendants by Michel Waldschmidt" (PDF). Bull. Amer. Math. Soc. 84 (8): 1370–1378. doi:10.1090/S0002-9904-1978-14584-4.