by J. W. S. Cassels

© Oxford University Press 2004 All rights reserved

**Mahler, Kurt** (1903-1988), mathematician, was born on 26 July 1903 in Krefeld in the Prussian Rhineland, with his twin sister, Hilde *(d.* 1934), the youngest of the eight children of Hermann Mahler (1855-1941) and his wife, Henriette, *née* Stern (1860-1942). Both parents were from the Jewish community; his father, a printer, owned a small business. The four oldest children died before Kurt was born. His brother Joseph, who inherited the printing business, died in a concentration camp, probably in 1945. The remaining child, Lydia *(d.* 1984), married and lived in the Netherlands.

Mahler was a sickly child and at five he developed tuberculosis of the right knee. Until the age of fourteen he had only four years of formal schooling. He then studied for two years in elementary technical schools and began an apprenticeship in a machine factory at Krefeld. During this time he became fascinated by mathematics and, entirely self-taught, was eventually reading books at university level. His work was brought to the attention of Felix Klein and his assistant Carl Siegel, and on their recommendation Mahler left the factory and was coached for university entrance while continuing his own mathematical studies.

In 1923 Mahler entered the University of Frankfurt am Main, where Siegel was then professor. Siegel went overseas in 1925 and Mahler migrated to the University of Göttingen; he received his doctorate in 1927 from Frankfurt, and remained at Göttingen for further research, supported by his parents and the Jewish community of Krefeld. At Göttingen he developed new methods in transcendence theory, including his celebrated classification of transcendental numbers, and his work on p-adic numbers contributed to their acceptance into general mathematical culture.

When Hitler came to power in 1933 Mahler had just been appointed assistant in the University of Königsberg, but had not yet taken up the post. Realizing that as a Jew he had no future in Germany, he left immediately for the Netherlands, proceeded to Manchester for the academic year 1933/4, supported by the modest Bishop Harvey Godwin fellowship, then, on a stipend raised by a Dutch Jewish group, spent two years at Groningen, where he developed an interest in the geometry of numbers. The cap of his tubercular knee was removed: over the next few years the infection disappeared, but he was left with a permanent limp. In 1937 he returned to Manchester, supported by small fellowships or temporary posts. While he was interned for three months at the outbreak of war, Manchester University awarded him the degree of ScD, and in 1941 an assistant lectureship, his first regular post. He lived from 1938 to 1958 in Donner House, Didsbury, a hostel for single university staff, and when it closed, bought himself a small suburban house.

In the following years Mahler developed his work on convex sets and quadratic forms into a geometry of numbers of general sets in n-dimensional space, including his influential compactness theorem. With his future now assured, Mahler moved steadily up the academic ladder. He took British nationality in 1946 and was elected to the Royal Society in 1948. The London Mathematical Society awarded him its senior Berwick prize in 1950, and its De Morgan medal in 1981; he was also a member of the Dutch and Australian mathematical societies. Manchester University created its first personal chair for him in 1952. Ten years later he went to Australia as professor at the Institute for Advanced Study in Canberra. This research post gave him freedom to travel and pursue his own studies, which he did with energy and enthusiasm. He also offered courses in number theory in the Australian National University. He was elected to the Australian Academy of Science in 1965 and received its Lyell medal in 1977. In 1968 he reached the statutory age of retirement, whereupon he took up a chair at Ohio State University, returning to Canberra in 1972 as emeritus professor. Mahler did not marry; an attraction of Canberra was that he could live in communal comfort at University House. Mahler was an excellent photographer, and kept up his knowledge of Chinese, begun in 1939 when he had considered taking up a post in China. He remained mathematically active until the end of his life. He died in Canberra at University House on 25 February 1988, leaving the bulk of his estate to the Australian Mathematical Society, which established a lectureship in his memory.

J. W. S. CASSELS

**Sources **

personal record, RS

K. Mahler, 'How I became a mathematician', *American Mathematical Monthly,* 81 (1974), 981-3

K. Mahler, 'Fifty years as a mathematician', *Journal of Number Theory,* 14 (1982), 121-55

J. H. Coates and A. J. van der Poorten, *Memoirs FRS,* 39 (1994), 263-79

J. W. S. Cassels, 'Obituary of Kurt Mahler', *Acta Arithmetica,* 58 (1991), 215-28 [with list of publications, pp. 229-37]

J. W. S. Cassels, *Bulletin of the London Mathematical Society,* 24 (1992), 381-97

**Archives **

Bodl. Oxf., Society for Protection of Science and Learning file

RS

Trinity Cam., corresp. with Harold Davenport, letters

**Likenesses **

W. Stoneman, photograph, 1948, NPG *[see illus.]*

photographs, RS

portrait, repro. in Cassels, *Acta Arithmetica*

portrait, repro. in J. W. S. Cassels, *Bulletin of the London Mathematical Society*

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