View source for Alan Baker (mathematician)

{{short description|English mathematician (1939–2018)}}
{{other people||Alan Baker (disambiguation){{!}}Alan Baker}}
{{Use dmy dates|date=June 2021}}
{{Use British English|date=May 2012}}
{{Infobox scientist
| name = Alan Baker
| honorific_suffix = {{postnom|country=GBR|size=100%|FRS}}
|image=Alan-Baker.jpg
| image_size = 250px
| caption = 
| birth_date = {{birth date|1939|08|19|df=y}}
| birth_place = London, England
| death_date = {{death date and age|2018|02|04|1939|08|19|df=y}}
| death_place = [[Cambridge]], England
| field = [[Mathematics]]
| work_institutions = [[University of Cambridge]]
| alma_mater = [[University College London]]<br>[[University of Cambridge]]
| doctoral_advisor = [[Harold Davenport]]
| doctoral_students = [[John Coates (mathematician)|John Coates]]<br>[[Yuval Flicker]]<br>[[Roger Heath-Brown]]<br>[[David Masser]]<br>[[Cameron Leigh Stewart|Cameron Stewart]]
| thesis_title = Some Aspects of Diophantine Approximation
| thesis_year = 1964
| known_for = [[Number theory]]<br>[[Diophantine equations]]<br>[[Baker's theorem]]<br>[[Stark–Heegner theorem|Baker–Heegner–Stark theorem]]
| prizes = [[Fields Medal]] (1970)<br>[[Adams Prize]] (1972)
| footnotes = 
}}
'''Alan Baker''' {{postnom|country=GBR|FRS}}<ref>{{Cite journal |last=Masser |first=David |date=2023 |title=Alan Baker. 19 August 1939—4 February 2018 |url=https://royalsocietypublishing.org/doi/10.1098/rsbm.2022.0033 |journal=Biographical Memoirs of Fellows of the Royal Society |volume=74|pages=9–36 |doi=10.1098/rsbm.2022.0033 |doi-access=free }}</ref> (19 August 1939 – 4 February 2018<ref>[https://www.trin.cam.ac.uk/news/tributes-paid-to-professor-alan-baker/ Trinity College website, retrieved 5 February 2018]</ref>) 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 School|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.<ref name="Whos Who">{{Who's Who | title=BAKER, Prof. Alan | id = U6216 | type = was | volume = 2019 | edition = online}}</ref> 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.<ref>[http://www.ias.edu/people/cos/frontpage?page=7 Institute for Advanced Study: A Community of Scholars] {{webarchive|url=https://web.archive.org/web/20130106144411/http://www.ias.edu/people/cos/frontpage?page=7 |date=6 January 2013 }}</ref> 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.<ref name="Whos Who"/>

His interests were in number theory, [[Transcendental number theory|transcendence]], [[linear forms in logarithms]], [[Effective results in number theory|effective methods]], [[Diophantine geometry]] and [[Diophantine analysis]].

In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-03.</ref> He has also been made a foreign fellow of [[the National Academy of Sciences, India]].<ref name=nasi>{{cite web|url=http://www.nasi.org.in/foreign.asp|title=National Academy of Sciences, India: Foreign Fellows|access-date=2 June 2018|archive-date=18 February 2017|archive-url=https://web.archive.org/web/20170218165325/http://www.nasi.org.in/foreign.asp|url-status=dead}}</ref>

==Research==
Baker generalised the [[Gelfond–Schneider theorem]], which itself is a solution to [[Hilbert's seventh problem]].<ref>Biography in Encyclopædia Britannica.
http://www.britannica.com/eb/article-9084909/Alan-Baker</ref> Specifically, Baker showed that if <math>\alpha_1,...,\alpha_n</math> are [[algebraic number]]s (besides 0 or 1), and if <math>\beta_1,..,\beta_n</math> are [[irrational number|irrational]] algebraic numbers such that the set <math>\{1,\beta_1,...,\beta_n\}</math> is [[linearly independent]] over the rational numbers, then the number <math>\alpha_1^{\beta_1}\alpha_2^{\beta_2}\cdots\alpha_n^{\beta_n}</math> is [[transcendental number|transcendental]].

Baker made significant contributions to several areas in number theory, such as the Gauss [[class number problem]],<ref name="Goldfeld 1985 class number problem">{{cite journal | last=Goldfeld | first=Dorian | title=Gauss' class number problem for imaginary quadratic fields | journal=Bulletin of the American Mathematical Society | publisher=American Mathematical Society (AMS) | volume=13 | issue=1 | year=1985 | issn=0273-0979 | doi=10.1090/s0273-0979-1985-15352-2 | pages=23–37| doi-access=free }}</ref> diophantine approximation, and to Diophantine equations such as the [[Mordell curve]].<ref name="Masser 2021 Alan Baker">{{cite journal | last=Masser | first=David | title=Alan Baker, FRS, 1939–2018 | journal=Bulletin of the London Mathematical Society | publisher=Wiley | volume=53 | issue=6 | year=2021 | issn=0024-6093 | doi=10.1112/blms.12553 | pages=1916–1949| s2cid=245627886 | doi-access=free }}</ref><ref name="Wüstholz 2019 Alan Baker">{{cite journal | last=Wüstholz | first=Gisbert | title=Obituary of Alan Baker FRS | journal=Acta Arithmetica | publisher=Institute of Mathematics, Polish Academy of Sciences | volume=189 | issue=4 | year=2019 | issn=0065-1036 | doi=10.4064/aa181211-14-12 | pages=309–345| s2cid=197494318 }}</ref>

==Selected publications==
*{{Citation | last1=Baker | first1=Alan | title=Linear forms in the logarithms of algebraic numbers. I | doi=10.1112/S0025579300003971 | mr=0220680 | year=1966 | journal=[[Mathematika]] | issn=0025-5793 | volume=13 | issue=2 | pages=204–216}}
*{{Citation | last1=Baker | first1=Alan | title=Linear forms in the logarithms of algebraic numbers. II | doi=10.1112/S0025579300008068 | mr=0220680 | year=1967a | journal=[[Mathematika]] | issn=0025-5793 | volume=14 | pages=102–107}}
*{{Citation | last1=Baker | first1=Alan | title=Linear forms in the logarithms of algebraic numbers. III | doi=10.1112/S0025579300003843  | mr=0220680 | year=1967b | journal=[[Mathematika]] | issn=0025-5793 | volume=14 | issue=2 | pages=220–228}}
*{{Citation | last1=Baker | first1=Alan | title=Transcendental number theory | url=https://books.google.com/books?isbn=052139791X | publisher=[[Cambridge University Press]] | edition=2nd | series=Cambridge Mathematical Library | isbn=978-0-521-39791-9 | mr=0422171 | year=1990}}; {{cite book|title=1st edition|year=1975}}<ref>{{cite journal|author=Stolarsky, Kenneth B.|title=Review: ''Transcendental number theory'' by Alan Baker; ''Lectures on transcendental numbers'' by Kurt Mahler; ''Nombres transcendants'' by Michel Waldschmidt|journal=Bull. Amer. Math. Soc.|year=1978|volume=84|issue=8|pages=1370–1378|url=https://www.ams.org/journals/bull/1978-84-06/S0002-9904-1978-14584-4/S0002-9904-1978-14584-4.pdf|doi=10.1090/S0002-9904-1978-14584-4|doi-access=free}}</ref>
*{{Citation | last1=Baker | first1=Alan | last2=Wüstholz | first2=G. | title=Logarithmic forms and Diophantine geometry | url=https://books.google.com/books?isbn=978-0-521-88268-2 | publisher=Cambridge University Press | series=New Mathematical Monographs | isbn=978-0-521-88268-2 | mr=2382891 | year=2007 | volume=9}}

==Honours and awards==
*1970: [[Fields Medal]]
*1972: [[Adams Prize]]
*1973: Fellowship of the [[Royal Society]]

==References==
{{reflist}}

==External links==
* {{MacTutor Biography|id=Baker_Alan|title=Alan Baker}}
* {{MathGenealogy |id=22765 |name=Alan Baker}}
* {{cite journal | last = Masser | first =David |date=January 2019 | title = Alan Baker 1939–2018 | journal = [[Notices of the American Mathematical Society]] | volume = 66 | issue = 1 | pages = 32–35 | doi =10.1090/noti1753 | url = https://www.ams.org/journals/notices/201901/rnoti-p32.pdf | doi-access = free }}
{{Fields medalists}}

{{Authority control}}

{{DEFAULTSORT:Baker, Alan}}
[[Category:1939 births]]
[[Category:2018 deaths]]
[[Category:20th-century English mathematicians]]
[[Category:21st-century English mathematicians]]
[[Category:Fields Medalists]]
[[Category:British number theorists]]
[[Category:Alumni of University College London]]
[[Category:Alumni of Trinity College, Cambridge]]
[[Category:Fellows of Trinity College, Cambridge]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the Royal Society]]
[[Category:Foreign fellows of the Indian National Science Academy]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Cambridge mathematicians]]
[[Category:Mathematicians from London]]