View source for Alexander Gelfond

{{Short description|Soviet mathematician}}
{{Distinguish|Israel Gelfand}}
{{family name hatnote|Osipovich|Gelfond|lang=Eastern Slavic}}

{{Infobox scientist
|name              = Alexander Gelfond
|image             =
|image_size       =250px
|caption           = Alexander Gelfond
|birth_date        =  24 October 1906
|birth_place       = [[Saint Petersburg]], Russian Empire
|death_date        = {{death-date and age|7 November 1968|24 October 1906}}
|death_place       =  [[Moscow]], Soviet Union
|residence         =
|citizenship       =  Soviet Union
|nationality       =  Soviet Union
|ethnicity         =
|field             = [[Mathematics]]
|work_institutions = Moscow State University <br /> [[Steklov Mathematical Institute]]
|alma_mater        = [[Moscow State University]]
|doctoral_advisor  = [[Aleksandr Yakovlevich Khinchin|Alexander Khinchin]] <br /> [[Vyacheslav Stepanov]]
|doctoral_students = [[Gregory Freiman]]
|known_for         = [[Gelfond's theorem]]
|author_abbrev_bot =
|author_abbrev_zoo =
|influences        =
|influenced        =
|prizes            =
|religion          =
|footnotes         =
|signature         =
}}
'''Alexander Osipovich Gelfond''' ({{langx|ru|Алекса́ндр О́сипович Ге́льфонд}}; 24{{nbsp}}October 1906{{snd}}7{{nbsp}}November 1968) was a [[Soviet Union|Soviet]] mathematician. [[Gelfond–Schneider theorem|Gelfond's theorem]], also known as the Gelfond–Schneider theorem, is named after him.

==Biography==

Alexander Gelfond was born in Saint Petersburg, [[Russian Empire]], the son of a professional [[physician]] and amateur [[philosopher]] [[Osip Gelfond]].<ref name="Yandell">{{cite book |last1=Yandell |first1=Ben |title=The Honors Class: Hilbert's Problems and Their Solvers |date=2001 |publisher=CRC Press |location=Boca Ranton |isbn=9781439864227 |url=https://books.google.com/books?id=3UBZDwAAQBAJ&q=%22Osip+Gelfond%27&pg=PA192 |language=en}}</ref> He entered [[Moscow State University]] in 1924, started his postgraduate studies there in 1927, and obtained his [[Doctor of Philosophy|Ph.D.]] in 1930. His advisors were [[Aleksandr Khinchin]] (1894-1959) and [[Vyacheslav Stepanov]] (1889-1950).<ref>{{Cite web |title=Aleksandr Osipovich Gelfond - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Gelfond/ |access-date=2024-11-26 |website=Maths History |language=en}}</ref><ref>{{Cite web |title=Aleksandr Gelfond - The Mathematics Genealogy Project |url=https://www.mathgenealogy.org/id.php?id=56858 |access-date=2024-11-26 |website=www.mathgenealogy.org}}</ref>

In 1930, he stayed for five months in [[Germany]] (in [[Berlin]] and [[Göttingen]]) where he worked with [[Edmund Landau]], [[Carl Ludwig Siegel]], and [[David Hilbert]]. In 1931 he started teaching as a Professor at the Moscow State University and worked there until the last day of his life. Since 1933 he also worked at the [[Steklov Institute of Mathematics]].

In 1939, he was elected a [[Corresponding member]] of the [[Academy of Sciences of the Soviet Union]] for his works in the field of [[Cryptography]]. According to [[Vladimir Arnold]], during [[World War II]] Gelfond was the Chief Cryptographer of the [[Soviet Navy]].<ref>{{cite news |last=Arnold |first=Vladimir |script-title=ru:Владимир Арнольд: "Опасаться компетентных соперников очень естественно для начальников" |url=http://young-science.ru/sections/expertise/31-qq/1898-l-0q---.html |newspaper=[[Gazeta.ru]] |date=3 June 2006 |author-link=Vladimir Arnold |language=ru |archive-url=https://web.archive.org/web/20100610052252/http://www.gzt.ru/topnews/education/-vladimir-arnoljd-opasatjsya-kompetentnyh-/308825.html |archive-date=10 June 2010 |url-status=dead |access-date=10 August 2011 }}</ref>

==Results==
Gelfond obtained important results in several mathematical domains including [[number theory]], [[theory of analytic functions|analytic functions]], [[integral equation]]s, and the [[history of mathematics]], but his most famous result is his [[Gelfond's theorem|eponymous theorem]]:
{{block indent|1=If {{mvar|α}} and {{mvar|β}} are [[algebraic number]]s (with {{math|''α'' ≠ 0}} and {{math|''α'' ≠ 1}}), and if {{mvar|β}} is not a [[real number|real]] [[rational number]], then any value of {{math|''α''<sup>''β''</sup>}} is a [[transcendental number]].}}

This is the famous [[Hilbert's seventh problem|7th Hilbert's problem]]. Gelfond proved a special case of the theorem in 1929 when he was a postgraduate student and fully proved it in 1934. The same theorem was independently proven by [[Theodor Schneider]], and so the theorem is often known as the [[Gelfond–Schneider theorem]]. In 1929 Gelfond proposed an extension of the theorem known as  [[Gelfond's conjecture]] that was proven by [[Alan Baker (mathematician)|Alan Baker]] in 1966.

Before Gelfond's works only a few numbers such as {{mvar|[[E (mathematical constant)|e]]}} and [[Pi|{{pi}}]] were known to be transcendental. After his works, an infinite number of transcendentals could be easily obtained. Some of them are named in Gelfond's honor:
*{{math|2{{sup|{{sqrt|2}}}}}} is known as the [[Gelfond–Schneider constant]]
*{{math|''e''{{sup|''π''}}}} is known as [[Gelfond's constant]].

==Notes==
{{Reflist}}

==References==
*{{Cite book|last1=Gel'fond|first1=A. O.|title=Transcendental and algebraic numbers|orig-year=1952 | url=https://books.google.com/books?isbn=0486495264|publisher=[[Dover Publications]]|location=New York|series=Dover Phoenix editions|isbn=978-0-486-49526-2|mr=0057921|year=1960}}
*{{cite journal|author1=B. V. Levin |author2=N. I. Feldman |author3=A. B. Sĭdlovsky | title= Alexander O. Gelfond|journal=[[Acta Arithmetica]]|year=1971| volume=17|issue=4 |pages=315–336|doi=10.4064/aa-17-4-315-336 |url=http://matwbn.icm.edu.pl/ksiazki/aa/aa17/aa1741.pdf |access-date=2017-02-12|doi-access=free}}
*{{MacTutor|id=Gelfond}}

==External links==
*{{MathGenealogy |id=56858}}

{{Authority control}}

{{DEFAULTSORT:Gelfond, Alexander Osipovich}}
[[Category:1906 births]]
[[Category:1968 deaths]]
[[Category:Mathematicians from Saint Petersburg]]
[[Category:People from Sankt-Peterburgsky Uyezd]]
[[Category:Russian Jews]]
[[Category:Soviet mathematicians]]
[[Category:Number theorists]]
[[Category:Russian cryptographers]]
[[Category:Moscow State University alumni]]
[[Category:Academic staff of Moscow State University]]
[[Category:Corresponding Members of the USSR Academy of Sciences]]
[[Category:Recipients of the Order of Lenin]]
[[Category:Recipients of the Order of the Red Banner of Labour]]
[[Category:Russian scientists]]