# Felix Hausdorff

Hausdorff ranks among the preeminent German mathematicians of the early 20th century.

He was born on 8 November 1868 in Breslau as the son of a Jewish merchant. From 1870 the family lived in Leipzig, where Hausdorff completed his schooling and the major part of his studies. In 1895 he was awarded his habilitation at the University of Leipzig where he taught, first as a lecturer and then from 1901-1910 as an unofficial associate professor. He was appointed associate professor in Bonn in 1910 and assumed a full professorship in 1913 in Greifswald. He returned to Bonn in 1921 to continue his work until 1935. During the national socialist regime, he suffered increasing harassment and humiliation until 26 Januar 1942, when he and his wife chose suicide over imminent deportation to a concentration camp.

## Mathematical work

With his masterpiece *Grundzüge der Mengenlehre* (1914), Hausdorff established topology as an independent discipline in mathematics. This book was also a milestone on the way to modern set theory based mathematics of the 20th century.

In addition, Hausdorff made significant contributions to general and descriptive set theory (Hausdorff recursion formula for the aleph exponentiation, higher theory of ordered sets, beginning of the theory on saturated structures, solution to the continuum hypothesis for Borel sets), measure theory (Hausdorff mass and Hausdorff dimension, sphere paradox), algebra (Baker-Campbell-Hausdorff formula), functional anaylsis (Hausdorff limit theorems and problems of moments, Hausdorff-Young inequality), probability theory (semi-invariants, Gram-Charlier series, first correct proof of the strong law of large numbers), and insurance mathematics (first correct proof of the Hattendorff theorem, individual risk theory).

## Literary and philosophical work

Hausdorff pursued, especially during the early years in Leipzig, a kind of double identity: as Felix Hausdorff, the productive mathematician, and as Paul Mongré. Under this pseudonym, Hausdorff enjoyed remarkable recognition within the German intelligentsia at the end of the 19th century as a writer, philosopher and socially critical essayist. He fostered a circle of friends that consisted of well known writers, artists and publishers including Hermann Conradi, Richard Dehmel, Otto Erich Hartleben, Gustav Kirstein, Max Klinger, Max Reger and Frank Wedekind. Between 1897 and 1904, Hausdorff reached the peak of his literary-philosophical accomplishment: during this period, 18 of a total of 22 works were published under his pseudonym. These included the volume of aphorisms *Sant’ Ilario: Thoughts from Zarathrustra’s Country*, his critique *Das Chaos in kosmischer Auslese*, a book of poems entitled *Ekstases*, the farce *Der Arzt seiner Ehre*, as well as numerous essays, most of which appeared in the leading journal of the day, “Neue Deutsche Rundschau (Freie Bühne)”. The play was Hausdorff’s greatest literary success, as it was performed over 300 times in 31 cities.

## Collected works

Within the framework of a project under the auspices of the North Rhine-Westfalia Academy of Sciences, the Mathematics Institute of the University of Bonn is publishing the collected works of Felix Hausdorff. These include his philosophical and literary writings, his correspondence, and selected items from his estate. Six of the planned nine volumes have already appeared in Springer Verlag.

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