Henry Mann

Henry Berthold Mann , originally Heinrich Mann, (born October 27, 1905 in Vienna , † February 1, 2000 in Tucson ) was an American mathematician who dealt with statistics, combinatorics, algebra and number theory.

life and work

Mann received his doctorate in 1935 at the University of Vienna under Philipp Furtwängler with a thesis on algebraic number theory (representation of the relatively prime residual classes according to prime ideal power modules using an independent basis). After a year as a school teacher and then as a tutor and researcher (as a Jew he could not get a job at the time) he emigrated to the USA in 1938. There, too, he initially worked as a tutor, but already published on statistics, especially the statistical design of experiments, about which he wrote a book in 1949. In 1941 he received a Carnegie Fellowship to study mathematical statistics with Abraham Wald at Columbia Universityto work. In 1943/44 he was an instructor at Bard College in Annendale in New York. After research positions at Ohio State University (1944/45) and Brown University (1945), he was Associate Professor at Ohio State in 1946 and full professor in 1948. In 1964 he retired from Ohio State and became a professor at the University of Wisconsin (where he was previously visiting professor and researched for the Army Mathematical Research Center) and in 1971 at the University of Arizona in Tucson. In 1975 he finally retired.

In 1949/50 he was visiting professor at the University of California, Berkeley .

In 1941 he proved a conjecture by Lew Schnirelmann and Edmund Landau in additive number theory, about which he had heard in a lecture by Alfred Brauer . For this he received the Cole Prize in number theory in 1946 . Also known as the ( ) hypothesis, the theorem states that if and are subsets of the natural numbers , then the direct sum holds ${\ displaystyle \ alpha + \ beta}$ ${\ displaystyle A}$ ${\ displaystyle B}$ ${\ displaystyle \ mathbb {N}}$ ${\ displaystyle A \ oplus B \ neq \ mathbb {N}}$

{\ displaystyle \ sigma (A \ oplus B) \ geq \ sigma (A) + \ sigma (B)}

.

Here are the Schnirelmann densities of subsets ${\ displaystyle \ sigma}$

{\ displaystyle \ sigma (A) = \ inf _ {n \ in \ mathbb {N}} {\ frac {A (n)} {n}}}

and A (n) the number of elements of A less than or equal to n.

In addition, he dealt with combinatorics, algebraic number theory, group theory and Galois theory, statistics and probability theory.

He had been married since 1935 and had a son.

Fonts

Analysis and Design of Experiments. Dover, New York 1949
Introduction to algebraic number theory. Ohio State University Press 1955
Addition Theorems: the addition theorem of group theory and number theory. Wiley 1965

literature

Maximilian Pinl , Auguste Dick : Colleagues in a Dark Time , Annual Report DMV, Volume 75, 1973, p. 196

Web links

Remarks

^ Mann: A proof of the fundamental theorem on the density of sums of sets of positive integers. Annals of Mathematics, Series 2, Vol. 43, 1942, pp. 523-527. The problem and the solution of man be in Khinchin: Three pearls of number theory treated
↑ The set of all sums with and ${\ displaystyle a + b}$ ${\ displaystyle a \ in A}$ ${\ displaystyle b \ in B}$

personal data
SURNAME	Man, henry
ALTERNATIVE NAMES	Husband, Henry Berthold (full name); Man, Heinrich
BRIEF DESCRIPTION	American mathematician and university professor
DATE OF BIRTH	October 27, 1905
PLACE OF BIRTH	Vienna
DATE OF DEATH	February 1, 2000
Place of death	Tucson

[1] Mann: A proof of the fundamental theorem on the density of sums of sets of positive integers. Annals of Mathematics, Series 2, Vol. 43, 1942, pp. 523-527. The problem and the solution of man be in Khinchin: Three pearls of number theory treated

[2] The set of all sums with and ${\ displaystyle a + b}$ ${\ displaystyle a \ in A}$ ${\ displaystyle b \ in B}$