# Alan Baker (mathematician)

Alan Baker

Born 19 August 1939
London, England
Died 4 February 2018 (aged 78)
Cambridge, England
Nationality British
Alma mater University College London
University of Cambridge
Known for Number theory
Diophantine equations
Baker's theorem
Awards Fields Medal (1970)
Scientific career
Fields Mathematics
Institutions University of Cambridge
Thesis Some Aspects of Diophantine Approximation (1964)
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.

## 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] He has also been made a foreign fellow of the National Academy of Sciences, India.[4]

## Accomplishments

Baker generalized the Gelfond–Schneider theorem, itself a solution to Hilbert's seventh problem.[5] Specifically, Baker showed that if ${\displaystyle \alpha _{1},...,\alpha _{n}}$ are algebraic numbers (besides 0 or 1), and if ${\displaystyle \beta _{1},..,\beta _{n}}$ are irrational algebraic numbers such that the set ${\displaystyle \{1,\beta _{1},...,\beta _{n}\}}$ are linearly independent over the rational numbers, then the number ${\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}}$ 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. [6]
• 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. ^ Trinity College website, accessed 5 February 2018
2. ^ Institute for Advanced Study: A Community of Scholars Archived 6 January 2013 at the Wayback Machine.
3. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
4. ^ "National Academy of Sciences, India: Foreign Fellows". Retrieved 2 June 2018.
5. ^ Biography in Encyclopædia Britannica. http://www.britannica.com/eb/article-9084909/Alan-Baker
6. ^ 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.