Alan Baker (mathematician)

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

Alan Baker
Alan Baker
Born	(1939-08-19) 19 August 1939 London, England
Nationality	British
Fields	Mathematics
Institutions	University of Cambridge
Alma mater	University College London University of Cambridge
Thesis	Some Aspects of Diophantine Approximation (1964)
Doctoral advisor	Harold Davenport
Doctoral students	John Coates Yuval Flicker Roger Heath-Brown Richard Clive Mason David Masser Robert Odoni Cameron Stewart
Known for	Number theory Diophantine equations Baker's theorem
Notable awards	Fields Medal (1970) Adams Prize (1972)

Alan Baker, FRS (born 19 August 1939) is 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. He was a visiting scholar at the Institute for Advanced Study in the fall of 1970.^[1] He is a fellow of Trinity College, Cambridge.

His interests are in number theory, transcendence, logarithmic form, effective methods, Diophantine geometry and Diophantine analysis.

In 2012 he became a fellow of the American Mathematical Society.^[2]

Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.^[3] 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. ^[4]
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

References

↑ Institute for Advanced Study: A Community of Scholars
↑ List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
↑ Biography in Encyclopaedia 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

Fields Medalists

1936 Ahlfors Douglas 1950 Schwartz Selberg 1954 Kodaira Serre 1958 Roth Thom 1962 Hörmander Milnor 1966 Atiyah Cohen Grothendieck Smale 1970 Baker Hironaka Novikov Thompson 1974 Bombieri Mumford 1978 Deligne Fefferman Margulis Quillen 1982 Connes Thurston Yau 1986 Donaldson Faltings Freedman 1990 Drinfeld Jones Mori Witten 1994 Bourgain Lions Yoccoz Zelmanov 1998 Borcherds Gowers Kontsevich McMullen 2002 Lafforgue Voevodsky 2006 Okounkov Perelman Tao Werner 2010 Lindenstrauss Ngô Smirnov Villani 2014 Avila Bhargava Hairer Mirzakhani

Book Category Mathematics portal

Authority control	WorldCat Identities VIAF: 109057795 LCCN: n82247190 ISNI: 0000 0001 1081 6386 GND: 134145275 SUDOC: 081078072 BNF: cb12338485t (data) BIBSYS: 3023776 MGP: 22765 NLA: 35138746 ICCU: IT\ICCU\UBOV\581573

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