Hans Adolph Rademacher (; 3 April 1892 – 7 February 1969) was a German-born American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, known for work in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Biography

Rademacher received his Ph.D. in 1916 from Georg-August-Universität Göttingen;

Constantin Carathéodory Constantin Carathéodory (; 13 September 1873 – 2 February 1950) was a Greeks, Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, ...

supervised his dissertation. In 1919, he became '' privatdozent'' under

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

. In 1922, he became an assistant professor at the

University of Hamburg The University of Hamburg (, also referred to as UHH) is a public university, public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('':de:Allgemeines Vorlesungswesen, ...

, where he supervised budding mathematicians like Theodor Estermann. He was dismissed from his position at the University of Breslau by the

Nazi Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...

s in 1933 due to his public support of the

Weimar Republic The Weimar Republic, officially known as the German Reich, was the German Reich, German state from 1918 to 1933, during which it was a constitutional republic for the first time in history; hence it is also referred to, and unofficially proclai ...

, and emigrated from Europe in 1934. After leaving Germany, he moved to

Philadelphia Philadelphia ( ), colloquially referred to as Philly, is the List of municipalities in Pennsylvania, most populous city in the U.S. state of Pennsylvania and the List of United States cities by population, sixth-most populous city in the Unit ...

and worked at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

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 In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

, mathematical

genetics Genetics is the study of genes, genetic variation, and heredity in organisms.Hartl D, Jones E (2005) It is an important branch in biology because heredity is vital to organisms' evolution. Gregor Mendel, a Moravian Augustinians, Augustinian ...

, 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

, 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.

Works

* with Otto Toeplitz: ''Von Zahlen und Figuren.'' 1930. 2nd edn. 1933. Springer 2001, . * '' The Enjoyment of Mathematics''. ''Von Zahlen und Figuren'' translated into English by Herbert Zuckerman, Princeton University Press, 1957 * with

Ernst Steinitz Ernst Steinitz (13 June 1871 – 29 September 1928) was a German mathematician. Biography Steinitz was born in Laurahütte ( Siemianowice Śląskie), Silesia, Germany (now in Poland), the son of Sigismund Steinitz, a Jewish coal merchant, and ...

''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.'' 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.

References

External links

* * {{DEFAULTSORT:Rademacher, Hans 1892 births 1969 deaths 20th-century American mathematicians Mathematics popularizers Emigrants from Nazi Germany to the United States 20th-century German mathematicians Number theorists Mathematical analysts University of Pennsylvania faculty Mathematicians at the University of Pennsylvania New York University faculty University of Göttingen alumni Academic staff of the University of Breslau People from Wandsbek Academics from Hamburg Academic staff of the University of Hamburg Academic staff of the Humboldt University of Berlin