Robert Hermann Breusch (April 2, 1907 – March 29, 1995) was a German-American number theorist, the William J. Walker Professor of Mathematics at Amherst College.[1] [2]
Breusch was born in Freiburg, Germany, and studied mathematics both at the University of Freiburg and the University of Berlin.[1] [3] 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.[1] [4] They married there, and Breusch found a faculty position at Federico Santa María Technical University in Valparaiso.[1] In 1939, they left Chile for the United States, inviting Robert Frucht to take Breusch's place at Santa María;[5] 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.[1] [2] The Robert H. Breusch Prize in Mathematics, for the best senior thesis from an Amherst student, was endowed in his memory.[1]
As a mathematician, Breusch was known for his new proof of the prime number theorem[1] [6] and for the many solutions he provided to problems posed in the American Mathematical Monthly.[1] 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.[3] [7] [8] For instance, he proved that for n > 47 there is at least one prime between n and (9/8)n. He also wrote a calculus textbook, Calculus and Analytic Geometry with Applications (Prindle, Weber & Schmidt, 1969) with C. Stanley Ogilvy.