Alexander Osipovich Gelfond (russian: Алекса́ндр О́сипович Ге́льфонд; 24 October 1906 – 7 November 1968) was a
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
mathematician.
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 Russian Empire was an empire and the final period of the List of Russian monarchs, Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended th ...
, the son of a professional
physician
A physician (American English), medical practitioner (Commonwealth English), medical doctor, or simply doctor, is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through th ...
and amateur
philosopher Osip Gelfond Osip Isaakovich Gelfond (russian: link=no, Осип Ге́льфонд) (1868–1942) was a Russian physician and Marxist philosopher.
Osip studied at the University of Sorbonne, gaining a medical degree in 1896. He married Musia Gershevna in 1899, ...
.
He entered the
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
in 1924, started his postgraduate studies there in 1927 and obtained his
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
Entertainment
* '' PhD: Phantasy Degree'', a Korean comic series
* ''Piled Higher and Deeper
''Piled Higher and Deeper'' (also known as ''PhD Comics''), is a newsp ...
in 1930. His advisors were
Aleksandr Khinchin
Aleksandr Yakovlevich Khinchin (russian: Алекса́ндр Я́ковлевич Хи́нчин, french: Alexandre Khintchine; July 19, 1894 – November 18, 1959) was a Soviet mathematician and one of the most significant contributors to t ...
and
Vyacheslav Stepanov
Vyacheslav Vassilievich Stepanov (Вячеслав Васильевич Степанов; 4 September 1889, Smolensk – 22 July 1950, Moscow) was a mathematician, specializing in analysis. He was from the Soviet Union.
Stepanov was the son o ...
.
In 1930 he stayed for five months in
Germany
Germany, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...
(in
Berlin
Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ...
and
Göttingen
Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...
) where he worked with
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis.
Biography
Edmund Landau was born to a Jewish family in Berlin. His father was Leopo ...
,
Carl Ludwig Siegel
Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation ...
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
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part ...
.
In 1939 he was elected a
Corresponding member of the
Academy of Sciences of the Soviet Union
The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...
for his works in the field of
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ...
. According to
Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov– ...
, during
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
Gelfond was the Chief Cryptographer of the
Soviet Navy.
Results
Gelfond obtained important results in several mathematical domains including
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
,
analytic functions
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...
,
integral equation
In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n ...
s and the
history of mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
, but his most famous result is his
eponymous theorem:
:If and are
algebraic number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the p ...
s (with and ), and if is not a
real
Real may refer to:
Currencies
* Brazilian real (R$)
* Central American Republic real
* Mexican real
* Portuguese real
* Spanish real
* Spanish colonial real
Music Albums
* ''Real'' (L'Arc-en-Ciel album) (2000)
* ''Real'' (Bright album) (201 ...
rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ra ...
, then any value of is a
transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and .
Though only a few classe ...
.
This is the famous
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 __NOTOC__
Theodor Schneider (7 May 1911, Frankfurt am Main – 31 October 1988, Freiburg im Breisgau) was a German mathematician, best known for providing proof of what is now known as the Gelfond–Schneider theorem.
Schneider studied from 19 ...
, and so the theorem is often known as the
Gelfond–Schneider theorem
In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers.
History
It was originally proved independently in 1934 by Aleksandr Gelfond and Theodor Schneider.
Statement
: If ''a'' and ''b'' ar ...
. In 1929 Gelfond proposed an extension of the theorem known as the
Gelfond's conjecture that was proven by
Alan Baker in 1966.
Before Gelfond's works only a few numbers such as and
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:
* is known as the
Gelfond–Schneider constant
The Gelfond–Schneider constant or Hilbert number is two to the power of the square root of two:
:2 = ...
which was proved to be a transcendental number by Rodion Kuzmin in 1930.
In 1934, Aleksandr Gelfond and Theodor Schneider independently ...
* is known as
Gelfond's constant
In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is , that is, raised to the power . Like both and , this constant is a transcendental number. This was first established by Gelfond and may now be considered as an applicati ...
.
Notes
References
*
*
*
External links
*
{{DEFAULTSORT:Gelfond, Alexander Osipovich
1906 births
1968 deaths
Mathematicians from Saint Petersburg
People from Sankt-Peterburgsky Uyezd
Russian Jews
Soviet mathematicians
Number theorists
Russian cryptographers
Moscow State University alumni
Moscow State University faculty
Corresponding Members of the USSR Academy of Sciences
Recipients of the Order of Lenin
Recipients of the Order of the Red Banner of Labour