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 ( uk, Меліто́поль, translit=Melitópol’, ; russian: Мелитополь; based on el, Μελιτόπολις - "honey city") is a List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Zaporizhz ...
,
Zaporizhia Oblast of southeastern
Ukraine
Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inv ...
.
He entered in 1936 the Faculty of Mathematics and Mechanics at the
University of Leningrad
Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...
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 (russian: Орден Красной Звезды, Orden Krasnoy Zvezdy) 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 193 ...
, the
Order of the Patriotic War
The Order of the Patriotic War (russian: Орден Отечественной войны, Orden Otechestvennoy voiny) is a Soviet military decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to partisan ...
(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 approximations, the theory of
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 ...
s,
and
Diophantine equation
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...
s.
In 1899, French mathematician
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Math ...
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.
Hermi ...
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
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 α≠0 and α≠1), and if β 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 α
β 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 ...
.
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