Robert Breusch
Encyclopedia
Robert Hermann Breusch was a German-American number theorist
, the William J. Walker Professor of Mathematics at Amherst College
.
Breusch was born in Freiburg
, Germany
, and studied mathematics both at the University of Freiburg
and the University of Berlin. Unable to secure a university position after receiving his doctorate, Breusch became a schoolteacher near Freiburg, where he met his future wife, Kate Dreyfuss; Breusch was Protestant, but Dreyfuss was Jewish, and the two of them left Nazi Germany for Chile
in the mid-1930s. They married there, and Breusch found a faculty position at Federico Santa María Technical University in Valparaiso
. In 1939, they left Chile for the United States, inviting Robert Frucht
to take Breusch's place at Santa María; after some years working again as a schoolteacher, Breusch found a position at Amherst College in 1943. He became the Walker professor in 1970, and retired to become an emeritus professor in 1973. The Robert H. Breusch Prize in Mathematics, for the best senior thesis from an Amherst student, was endowed in his memory.
As a mathematician, Breusch was known for his new proof of the prime number theorem
and for the many solutions he provided to problems posed in the American Mathematical Monthly
. His thesis work combined Bertrand's postulate with Dirichlet's theorem on arithmetic progressions
by showing that each of the progressions 3i + 1, 3i + 2, 4i + 1, and 4i + 3 (for i = 0, 1, 2, ...) contains a prime number
between x and 2x for every x ≥ 7. He also wrote a calculus
textbook, Calculus and Analytic Geometry with Applications (Prindle, Weber & Schmidt, 1969) with C. Stanley Ogilvy.
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, the William J. Walker Professor of Mathematics at Amherst College
Amherst College
Amherst College is a private liberal arts college located in Amherst, Massachusetts, United States. Amherst is an exclusively undergraduate four-year institution and enrolled 1,744 students in the fall of 2009...
.
Breusch was born in Freiburg
Freiburg
Freiburg im Breisgau is a city in Baden-Württemberg, Germany. In the extreme south-west of the country, it straddles the Dreisam river, at the foot of the Schlossberg. Historically, the city has acted as the hub of the Breisgau region on the western edge of the Black Forest in the Upper Rhine Plain...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, and studied mathematics both at the University of Freiburg
University of Freiburg
The University of Freiburg , sometimes referred to in English as the Albert Ludwig University of Freiburg, is a public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany.The university was founded in 1457 by the Habsburg dynasty as the...
and the University of Berlin. Unable to secure a university position after receiving his doctorate, Breusch became a schoolteacher near Freiburg, where he met his future wife, Kate Dreyfuss; Breusch was Protestant, but Dreyfuss was Jewish, and the two of them left Nazi Germany for Chile
Chile
Chile ,officially the Republic of Chile , is a country in South America occupying a long, narrow coastal strip between the Andes mountains to the east and the Pacific Ocean to the west. It borders Peru to the north, Bolivia to the northeast, Argentina to the east, and the Drake Passage in the far...
in the mid-1930s. They married there, and Breusch found a faculty position at Federico Santa María Technical University in Valparaiso
Valparaíso
Valparaíso is a city and commune of Chile, center of its third largest conurbation and one of the country's most important seaports and an increasing cultural center in the Southwest Pacific hemisphere. The city is the capital of the Valparaíso Province and the Valparaíso Region...
. In 1939, they left Chile for the United States, inviting Robert Frucht
Robert Frucht
Robert Wertheimer Frucht was a German-Chilean mathematician; his research specialty was graph theory and the symmetries of graphs....
to take Breusch's place at Santa María; after some years working again as a schoolteacher, Breusch found a position at Amherst College in 1943. He became the Walker professor in 1970, and retired to become an emeritus professor in 1973. The Robert H. Breusch Prize in Mathematics, for the best senior thesis from an Amherst student, was endowed in his memory.
As a mathematician, Breusch was known for his new proof of the prime number theorem
Prime number theorem
In number theory, the prime number theorem describes the asymptotic distribution of the prime numbers. The prime number theorem gives a general description of how the primes are distributed amongst the positive integers....
and for the many solutions he provided to problems posed in the American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
. His thesis work combined Bertrand's postulate with Dirichlet's theorem on arithmetic progressions
Dirichlet's theorem on arithmetic progressions
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other words, there are infinitely many primes which are...
by showing that each of the progressions 3i + 1, 3i + 2, 4i + 1, and 4i + 3 (for i = 0, 1, 2, ...) contains a prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
between x and 2x for every x ≥ 7. He also wrote a calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
textbook, Calculus and Analytic Geometry with Applications (Prindle, Weber & Schmidt, 1969) with C. Stanley Ogilvy.