Alan Baker (mathematician)
Alan Baker | |
---|---|
Born |
London, England |
19 August 1939
Died | 4 February 2018 Cambridge, England |
(aged 78)
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 | 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^{[1]}) was an English mathematician, known for his work on effective methods in number theory, in particular those arising from transcendental number theory.
Contents
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.^{[2]} 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.^{[3]}
Accomplishments
Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.^{[4]} 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.
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.^{[5]}
- 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
- 1970: Fields Medal
- 1972: Adams Prize
References
- ^ 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.
- ^ 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.
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
- 1939 births
- 2018 deaths
- 20th-century English mathematicians
- 21st-century English mathematicians
- Fields Medalists
- Number theorists
- Alumni of University College London
- Fellows of Trinity College, Cambridge
- Fellows of the American Mathematical Society
- Fellows of the Royal Society
- Foreign Fellows of the Indian National Science Academy
- Institute for Advanced Study visiting scholars
- Members of the Department of Pure Mathematics and Mathematical Statistics
- Mathematicians from London