Hans Rademacher

Hans Adolph Rademacher (German: [ˈʁaːdəmaxɐ]; 3 April 1892 – 7 February 1969) was a German-born American mathematician, known for work in mathematical analysis and number theory.

Hans Adolph Rademacher
Born	(1892-04-03)3 April 1892 Hamburg-Wandsbek, German Empire
Died	7 February 1969(1969-02-07) (aged 76) Haverford, Pennsylvania, U.S.
Education	University of Göttingen
Scientific career
Fields	Mathematics
Institutions	University of Berlin University of Hamburg University of Pennsylvania
Doctoral advisor	Constantin Carathéodory
Notable students	George Andrews Paul T. Bateman Leila Bram Theodor Estermann Emil Grosswald

Biography

Rademacher received his Ph.D. in 1916 from Georg-August-Universität Göttingen; Constantin Carathéodory supervised his dissertation.^[1] In 1919, he became privatdozent under Constantin Carathéodory at University of Berlin. In 1922, he became an assistant professor at the University of Hamburg, where he supervised budding mathematicians like Theodor Estermann.^[2] He was dismissed from his position at the University of Breslau by the Nazis in 1933 due to his public support of the Weimar Republic,^[3] and emigrated from Europe in 1934.

After leaving Germany, he moved to Philadelphia and worked at the University of Pennsylvania until his retirement in 1962; he held the Thomas A. Scott Professorship of Mathematics at Pennsylvania from 1956 to 1962. Rademacher had a number of well-known students, including George Andrews, Paul T. Bateman, Theodor Estermann and Emil Grosswald.

Research

Rademacher performed research in analytic number theory, mathematical genetics, the theory of functions of a real variable, and quantum theory. Most notably, he developed the theory of Dedekind sums. In 1937 Rademacher discovered an exact convergent series for the partition function P(n), the number of integer partitions of a number, improving upon Ramanujan's asymptotic non-convergent series and validating Ramanujan's supposition that an exact series representation existed.

Awards and honors

With his retirement from the University of Pennsylvania, a group of mathematicians provided the seed funding for The Hans A. Rademacher Instructorships, and honored him with an honorary degree as Doctor of Science.

Rademacher is the co-author (with Otto Toeplitz) of the popular mathematics book The Enjoyment of Mathematics, published in German in 1930 and still in print.^[4][5]

Works

• with Otto Toeplitz: Von Zahlen und Figuren. 1930. 2nd edn. 1933. Springer 2001, ISBN 3-540-63303-0.^[6]
• The Enjoyment of Mathematics. Von Zahlen und Figuren translated into English by Herbert Zuckerman, Princeton University Press, 1957^[7]
• with Ernst Steinitz Vorlesungen über die Theorie der Polyeder- unter Einschluss der Elemente der Topologie. Springer 1932, 1976.
• Generalization of the Reciprocity Formula for Dedekind Sums. In: Duke Math. Journal. Vol. 21, 1954, pp. 391–397.
• Lectures on analytic number theory. 1955.
• Lectures on elementary number theory. Blaisdell, New York 1964, Krieger 1977.
• with Grosswald: Dedekind sums. Carus Mathematical Monographs 1972.
• Topics in analytic number theory.^[8] ed. Grosswald. Springer Verlag, 1973 (Grundlehren der mathematischen Wissenschaften).
• Collected papers. 2 vols. ed. Grosswald. MIT press, 1974.
• Higher mathematics from an elementary point of view. Birkhäuser 1983.

Further reading

• George E. Andrews, David M. Bressoud, L. Alayne Parson (eds.) The Rademacher legacy to mathematics. American Mathematical Society, 1994.
• Lexikon bedeutender Mathematiker. Deutsch, Thun, Frankfurt am Main, ISBN 3-8171-1164-9.
• Tom Apostol: Introduction to Analytical number theory. Springer
• Tom Apostol: Modular functions and Dirichlet Series in Number Theory. Springer
• Berndt, Bruce C. (1992). "Hans Rademacher (1892–1969)" (PDF). Acta Arithmetica. 61 (3): 209–231. doi:10.4064/aa-61-3-209-225. Retrieved 2009-02-07. Obituary and list of publications.

See also

• Hadamard transform
• Rademacher's contour
• Rademacher complexity
• Rademacher function
• Rademacher–Menchov theorem
• Rademacher's series
• Rademacher system
• Rademacher distribution
• Rademacher's theorem

References

1. Hans Rademacher at the Mathematics Genealogy Project.
2. "Theodor Estermann - Biography". Maths History. Retrieved 2022-08-24.
3. Siegmund-Schultze, Reinhard (2009). Mathematicians fleeing from Nazi Germany: individual fates and global impact. Princeton University Press. p. 69. ISBN 978-0-691-14041-4..
4. The Enjoyment of Math Review by Allen Stenger, Mathematical Association of America
5. Oakley, C. O. (October 1957). "Recent publications: The Enjoyment of Mathematics". The American Mathematical Monthly. 64 (8): 603. doi:10.2307/2308857. JSTOR 2308857.
6. Wrinch, D. M. "Review: Von Zahlen und Figuren: Proven mathematischen Denkens für Liebhaber der Mathematik by Hans Rademacher, Otto Toeplitz" The Mathematical Gazette, vol. 16, no. 217, 1932, pp. 63–63. JSTOR, https://doi.org/10.2307/3608155. Accessed 11 Aug. 2022.
7. Benz, Harry E. "Review: The Enjoyment of Mathematics by Hans Rademacher, Otto Toeplitz" The Mathematics Teacher, vol. 50, no. 6, 1957, pp. 454–455. JSTOR, http://www.jstor.org/stable/27955473. Accessed 11 Aug. 2022.
8. Stark, H. M. (1975). "Review: Hans Rademacher, Topics in analytic number theory". Bull. Amer. Math. Soc. 81 (4): 663–672. doi:10.1090/s0002-9904-1975-13815-8.

External links

• O'Connor, John J.; Robertson, Edmund F. "Hans Rademacher". MacTutor History of Mathematics Archive. University of St Andrews.
• Hans Rademacher at the Mathematics Genealogy Project