Naum Il'ich Feldman (26 November 1918 – 20 April 1994) was a Soviet mathematician who specialized in number theory.
Life
Feldman was born on 26 November 1918 in
Melitopol
Melitopol is a city and municipality in Zaporizhzhia Oblast, southeastern Ukraine. It is situated on the Molochna River, which flows through the eastern edge of the city into the Molochnyi Lyman estuary. Melitopol is the second-largest city ...
,
Zaporizhia Oblast
Zaporizhzhia Oblast (), commonly referred to as Zaporizhzhia (), is an oblast (region) in south-east Ukraine. Its administrative centre is the city of Zaporizhzhia. The oblast covers an area of , and has a population of The oblast is an import ...
of southeastern
Ukraine
Ukraine is a country in Eastern Europe. It is the List of European countries by area, second-largest country in Europe after Russia, which Russia–Ukraine border, borders it to the east and northeast. Ukraine also borders Belarus to the nor ...
.
He entered in 1936 the Faculty of Mathematics and Mechanics at the
University of Leningrad where he specialized in number theory under the supervision of
Rodion O. Kuzmin. After his graduation in 1941, Feldman was called up by the army and served from October 1941 until the end of the World war II. For his service, he was awarded the
Order of the Red Star
The Order of the Red Star () was a military decoration of the Soviet Union. It was established by decree of the Presidium of the Supreme Soviet of the USSR of 6 April 1930 but its statute was only defined in decree of the Presidium of the ...
, the
Order of the Patriotic War
The Order of the Patriotic War () is a Soviet Union, Soviet military Order (decoration), decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to Partisan (military), partisans for heroic deeds in the Easte ...
(second class), and the medals
"For the Capture of Königsberg",
"For the Defence of Moscow",
.
After his demobilization, he started his PhD in 1946 at the Institute of Mathematics at the University of Moscow, under the supervision of
Alexander O. Gelfond, and he presented his Ph.D. thesis in 1949. In 1950, he became head of the Department of Mathematics of the
Ufimsky Oil Institute, where he was assigned until 1954. He lectured at the
Moscow Geological Prospecting Institute from 1954 to 1961.
From September 1961 Feldman worked at Moscow State University, first in the department of mathematical analysis, and then in the department of number theory. In 1974 he became Doctor of Science. Feldman got full professorship in 1980.
Feldman died on 20 April 1994.
Work
Feldman obtained important results in number theory. His main research area were the theory of
Diophantine approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria.
The first problem was to know how well a real number can be approximated ...
s, the theory of
transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are and . ...
s,
and
Diophantine equation ''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name:
*Diophantine approximation
In number theory, the study of Diophantine approximation deals with the approximation of real n ...
s.
In 1899, French mathematician
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability.
Biograp ...
strengthened the famous theorem of
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermite p ...
that proved in 1873 the transcendence of the number without having been specifically constructed for this purpose. Later different estimates of the measure of transcendence were considered for other numbers too. Feldman's mentor Gelfond obtained his most famous result in 1948 in his
eponymous theorem, also known as the
7th Hilbert's problem:
: If α and β are
algebraic number
In mathematics, an algebraic number is a number that is a root of a function, root of a non-zero polynomial in one variable with integer (or, equivalently, Rational number, rational) coefficients. For example, the golden ratio (1 + \sqrt)/2 is ...
s (with α≠0 and α≠1), and if β is not a
real
Real may refer to:
Currencies
* Argentine real
* Brazilian real (R$)
* Central American Republic real
* Mexican real
* Portuguese real
* Spanish real
* Spanish colonial real
Nature and science
* Reality, the state of things as they exist, rathe ...
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 (for example,
The set of all ...
, then any value of α
β is a
transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are and . ...
.
In 1949, Feldman further improved Gelfond's method to estimate of the measure of transcendence for logarithms of algebraic numbers and periods of elliptic curves.
Of special importance is his result from 1960 on the measure of the transcendence of the number
.
References
Bibliography
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{{DEFAULTSORT:Feldman, Naum Ilich
Soviet mathematicians
1918 births
1994 deaths