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
[
edit
]
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
[
edit
]
Baker generalised the
Gelfond?Schneider theorem
, which itself is a solution to
Hilbert's seventh problem
.
[7]
Specifically, Baker showed that if
are
algebraic numbers
(besides 0 or 1), and if
are
irrational
algebraic numbers such that the set
is
linearly independent
over the rational numbers, then the number
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
[
edit
]
- 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; Wustholz, 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
[
edit
]
References
[
edit
]
- ^
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
.
- ^
Wustholz, 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
.
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