Alan Baker (mathematician)
English mathematician (1939–2018)
For other people with the same name, see
Alan Baker .
Alan Baker FRS [1] (19 August 1939 – 4 February 2018[2] ) 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 attended Stratford Grammar School , East London, and his academic career started as a student of Harold Davenport , at University College London and later at Trinity College, Cambridge , where he received his PhD.[3] He was a visiting scholar at the Institute for Advanced Study in 1970 when he was awarded the Fields Medal at the age of 31.[4] In 1974 he was appointed Professor of Pure Mathematics at Cambridge University , a position he held until 2006 when he became an Emeritus . He was a fellow of Trinity College from 1964 until his death.[3]
His interests were in number theory, transcendence , linear forms in logarithms , effective methods , Diophantine geometry and Diophantine analysis .
In 2012 he became a fellow of the American Mathematical Society .[5] He has also been made a foreign fellow of the National Academy of Sciences, India .[6]
Research
Baker generalised the Gelfond–Schneider theorem , which itself is a solution to Hilbert's seventh problem .[7] Specifically, Baker showed that if
α α -->
1
,
.
.
.
,
α α -->
n
{\displaystyle \alpha _{1},...,\alpha _{n}}
are algebraic numbers (besides 0 or 1), and if
β β -->
1
,
.
.
,
β β -->
n
{\displaystyle \beta _{1},..,\beta _{n}}
are irrational algebraic numbers such that the set
{
1
,
β β -->
1
,
.
.
.
,
β β -->
n
}
{\displaystyle \{1,\beta _{1},...,\beta _{n}\}}
is linearly independent over the rational numbers, then the number
α α -->
1
β β -->
1
α α -->
2
β β -->
2
⋯ ⋯ -->
α α -->
n
β β -->
n
{\displaystyle \alpha _{1}^{\beta _{1}}\alpha _{2}^{\beta _{2}}\cdots \alpha _{n}^{\beta _{n}}}
is transcendental .
Baker made significant contributions to several areas in number theory, such as the Gauss class number problem ,[8] diophantine approximation, and to Diophantine equations such as the Mordell curve .[9] [10]
Selected publications
Baker, Alan (1966), "Linear forms in the logarithms of algebraic numbers. I", Mathematika , 13 (2): 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 (2): 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.[11]
Baker, Alan; Wüstholz, G. (2007), Logarithmic forms and Diophantine geometry , New Mathematical Monographs, vol. 9, Cambridge University Press, ISBN 978-0-521-88268-2 , MR 2382891
Honours and awards
References
^ Masser, David (2023). "Alan Baker. 19 August 1939—4 February 2018" . Biographical Memoirs of Fellows of the Royal Society . 74 .
^ Trinity College website, retrieved 5 February 2018
^ a b "BAKER, Prof. Alan" . Who's Who & Who Was Who . Vol. 2019 (online ed.). A & C Black. (Subscription or UK public library membership required.)
^ 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.
^ "National Academy of Sciences, India: Foreign Fellows" . Archived from the original on 18 February 2017. Retrieved 2 June 2018 .
^ Biography in Encyclopædia Britannica.
http://www.britannica.com/eb/article-9084909/Alan-Baker
^ Goldfeld, Dorian (1985). "Gauss' class number problem for imaginary quadratic fields" . Bulletin of the American Mathematical Society . 13 (1). American Mathematical Society (AMS): 23–37. doi :10.1090/s0273-0979-1985-15352-2 . ISSN 0273-0979 .
^ Masser, David (2021). "Alan Baker, FRS, 1939–2018" . Bulletin of the London Mathematical Society . 53 (6). Wiley: 1916–1949. doi :10.1112/blms.12553 . ISSN 0024-6093 . S2CID 245627886 .
^ Wüstholz, Gisbert (2019). "Obituary of Alan Baker FRS". Acta Arithmetica . 189 (4). Institute of Mathematics, Polish Academy of Sciences: 309–345. doi :10.4064/aa181211-14-12 . ISSN 0065-1036 . S2CID 197494318 .
^ 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
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