Alexander Osipovich Gelfond (; 24October 19067November 1968) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

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 that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

, the son of a professional

physician A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the Medical education, study, Med ...

and amateur

philosopher Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

Osip Gelfond Osip Isaakovich Gelfond () (1868–1942) was a Russian people, Russian physician and Marxist philosopher. Osip studied at the University of Paris, gaining a medical degree in 1896. He married Musia Gershevna in 1899, who had also recently graduated ...

. He entered

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

in 1924, started his postgraduate studies there in 1927, and obtained his Ph.D. in 1930. His advisors were Aleksandr Khinchin (1894-1959) and Vyacheslav Stepanov (1889-1950). In 1930, he stayed for five months in

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

(in

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

and

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) 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 David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

. 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 () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

. In 1939, he was elected a

Corresponding member The corresponding member is one of the possible membership types in some organizations, especially in the learned societies and scientific academies. This title existed or exist in the Soviet Union, GDR, Polish People's Republic, Czechoslovak S ...

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. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (un ...

for his works in the field of

Cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

. According to

Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...

, during

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

Gelfond was the Chief Cryptographer of the

Soviet Navy The Soviet Navy was the naval warfare Military, uniform service branch of the Soviet Armed Forces. Often referred to as the Red Fleet, the Soviet Navy made up a large part of the Soviet Union's strategic planning in the event of a conflict with t ...

Results

Gelfond obtained important results in several mathematical domains including

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

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 mathematical analysis, 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,\ldots,x_n ; u(x_1,x_2 ...

s, and the

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...

, but his most famous result is his eponymous theorem: 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, 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 Comments The values o ...

. In 1929 Gelfond proposed an extension of the theorem known as 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 * is known as Gelfond's constant.

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 Academic staff of Moscow State University Corresponding Members of the USSR Academy of Sciences Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Russian scientists