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
1
,
.
.
.
,
α
n
{\displaystyle \alpha _{1},...,\alpha _{n}}
are
algebraic numbers (besides 0 or 1), and if
β
1
,
.
.
,
β
n
{\displaystyle \beta _{1},..,\beta _{n}}
are
irrational algebraic numbers such that the set
{
1
,
β
1
,
.
.
.
,
β
n
}
{\displaystyle \{1,\beta _{1},...,\beta _{n}\}}
is
linearly independent over the rational numbers, then the number
α
1
β
1
α
2
β
2
⋯
α
n
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
International National Academics People Other