Alan Baker (mathematician)

Alan Baker
Alan Baker
Born	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

1. Institute for Advanced Study: A Community of Scholars
2. List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
3. Biography in Encyclopaedia Britannica. http://www.britannica.com/eb/article-9084909/Alan-Baker
4. 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 (mathematician)", MacTutor History of Mathematics archive, University of St Andrews.
• Alan Baker at the Mathematics Genealogy Project