Alan Baker (mathematician)
Alan Baker  

Alan Baker


Born 
London, England 
19 August 1939
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 HeathBrown David Masser Cameron Stewart 
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.
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. 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 forms, 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 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 00255793, MR 0220680
 Baker, Alan (1967a), "Linear forms in the logarithms of algebraic numbers. II", Mathematika, 14: 102–107, doi:10.1112/S0025579300008068, ISSN 00255793, MR 0220680
 Baker, Alan (1967b), "Linear forms in the logarithms of algebraic numbers. III", Mathematika, 14: 220–228, doi:10.1112/S0025579300003843, ISSN 00255793, MR 0220680
 Baker, Alan (1990), Transcendental number theory, Cambridge Mathematical Library (2nd ed.), Cambridge University Press, ISBN 9780521397919, MR 0422171; 1st edition. 1975.^{[4]}
 Baker, Alan; Wüstholz, G. (2007), Logarithmic forms and Diophantine geometry, New Mathematical Monographs, 9, Cambridge University Press, ISBN 9780521882682, MR 2382891
Honours and awards
 1970: Fields Medal
 1972: Adams Prize
References
 ^ 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 20121103.
 ^ Biography in Encyclopædia Britannica. http://www.britannica.com/eb/article9084909/AlanBaker
 ^ 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/S000299041978145844.
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
 Living people
 20thcentury English mathematicians
 21stcentury 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