**Hans Rademacher** was a German-born mathematician who worked in analytic number theory, mathematical genetics, the theory of functions of a real variable and quantum theory.

- Hans grew up with broad interests; he both enjoyed and had a talent for modern languages, was interested in both natural and mathematical sciences, but by the time he was eighteen his main interest was in philosophy.
- Rademacher was awarded his doctorate in 1917.
- Of the mathematical research undertaken by Rademacher during this period, he is remembered most for the system of orthogonal functions (now known as Rademacher functions) which he introduced in a paper which was published in 1922.
- By the time the paper appeared he had already written a second paper on the completion of the system of Rademacher functions but he was advised not to publish it.
- Rademacher changed his area of mathematical interest from the theory of real functions to number theory in 1922 when he accepted the position of extraordinary professor at the University of Hamburg.
- He was led towards number theory by Hecke who had been appointed to Hamburg three years before Rademacher.
- In April 1925 Rademacher left Hamburg to become an ordinary professor at Breslau.
- It was a difficult decision for Rademacher, particularly since Hecke was so keen for him to stay in Hamburg.
- Had Hecke succeeded in his attempt to get Hamburg to offer Rademacher an ordinary professorship then he would almost certainly have remained there, but the university would not make the offer that Hecke requested and, after much thought, Rademacher went to Breslau.
- Normal expectations were completely overturned for most people and in particular for Rademacher the expectation that he would remain in Breslau vanished.
- Despite this, Rademacher was ever after to remain loyal to the University of Pennsylvania for providing him refuge from the horror that had engulfed his native land.
- 1947 was also the year in which Rademacher's second marriage also ended in divorce.
- Rademacher's early arithmetical work dealt with applications of Brun's sieve method and with the Goldbach problem in algebraic number fields.
- Rademacher also wrote important papers on Dedekind sums and investigated many problems relating to algebraic number fields.
- In December 1938 Rademacher was invited to lecture to the American Mathematical Society and he lectured on Fourier expansions of modular forms and problems of partition which surveyed work on modular forms of positive dimension and the resulting formulas for partition functions.
- Three years later Rademacher was again invited to address the American Mathematical Society and this time he chose the topic Trends in research: the analytic number theory.
- Rademacher was invited to deliver an address to the International Congress of Mathematicians in Cambridge, Massachusetts, in 1950.
- We mentioned above that Rademacher's second marriage ended in divorce in 1947 and he moved from Swarthmore to Philadelphia.
- Although he remained at the University of Pennsylvania for the rest of his career, Rademacher did spend time in other places, such as a semester at the Institute for Advanced Study at Princeton in 1953, the Tata Institute of Fundamental Research in Bombay in 1954-55 and also at the University of Göttingen during the same academic year.
- Rademacher was invited to be Hedrick Lecturer for the summer meeting of the Mathematical Association of America in Boulder, Colorado, in 1963.
- Rademacher did not edit his notes for publication before his death but had asked Grosswald to edit them for publication.
- The book Topics in analytic number theory was also published after Rademacher's death.
- Rademacher's books have continued to be widely read by students and researchers and are models of clarity.

Born 3 April 1892, Wandsbeck (part of Hamburg), Schleswig-Holstein, Germany. Died 7 February 1969, Haverford, Pennsylvania, USA.

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Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive