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 List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

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 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 the Great Northern War. ...

, 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 A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

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 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'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

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 th ...

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 of ...

. In 1930 he stayed for five months in

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

(in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

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, Carl Ludwig Siegel and

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

. 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 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 adver ...

. According to Vladimir Arnold, 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 vast majority of the world's countries—including all of the great powers—forming two opposin ...

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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

, analytic functions, integral equations and the history of mathematics, 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 po ...

s (with and ), and if is not a real

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 ration ...

, 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 classes ...

. 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 : If ''a'' and ''b'' are ...

. 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 prov ...

* 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 application ...

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