Robert Breusch
Robert Hermann Breusch (April 2, 1907 – March 29, 1995) was an 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 Valparaíso.[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.
See also
[edit]References
[edit]- 1 2 3 4 5 6 7 8 Armacost, David; Denton, James; Romer, Robert; Towne, Dudley, "Robert Breusch", Memorial Minutes, Amherst College, retrieved 2010-04-24.
- 1 2 Brief biography (in German), German Mathematical Society, retrieved 2010-04-24.
- 1 2 Robert Breusch at the Mathematics Genealogy Project.
- ↑ Siegmund-Schultze, Reinhard (2009), Mathematicians fleeing from Nazi Germany: individual fates and global impact, Princeton University Press, p. 131, ISBN 978-0-691-14041-4.
- ↑ Biography of Frucht (in Spanish), Walter Gaete and Raúl González, retrieved 2010-04-22.
- ↑ Breusch, R. (1954), "Another proof of the prime number theorem", Duke Mathematical Journal, 21 (1): 49–53, doi:10.1215/S0012-7094-54-02106-7, MR 0068567.
- ↑ Breusch, R. (1932), "Zur Verallgemeinerung des Bertrandschen Postulates, daß zwischenx und 2x stets Primzahlen liegen", Mathematische Zeitschrift (in German), 34 (1): 505–526, doi:10.1007/BF01180606, S2CID 121351858.
- ↑ Shorey, T. N.; Tijdeman, R. (1990), "On the greatest prime factor of an arithmetical progression", in Baker, Alan; Bollobás, Béla; Hajnal, A. (eds.), A Tribute to Paul Erdős, Cambridge University Press, pp. 385–390, ISBN 978-0-521-38101-7.
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