**Hausdorff** worked in topology creating a theory of topological and metric spaces. He also worked in set theory and introduced the concept of a partially ordered set.

- They achieved this, but only after quite an effort for Felix had his heart set on the idea, and after this he turned towards mathematics as the subject to study at university.
- Hausdorff studied at Leipzig University under Heinrich Bruns and Adolph Mayer, graduating in 1891 with a doctorate in applications of mathematics to astronomy.
- However Hausdorff's main interests were in literature and philosophy and his circle of friends consisted almost entirely of writers and artists, such as the composer Max Reger, rather than scientists.
- Although still a Privatdozent, Hausdorff was well off, so marriage at this stage in his career presented no financial difficulties.
- This clearly indicates that at this time Hausdorff was keener to remain in his literary and artistic circle in Leipzig than he was to progress his career in mathematics.
- After 1904 Hausdorff began working in the area for which he is famous, namely topology and set theory.
- Hausdorff proved further results on the cardinality of Borel sets in 1916.
- Hausdorff taught at Leipzig until 1910 when he went to Bonn.
- It was Study who in many ways motivated Hausdorff to become more involved in both mathematical research and also in developing his career in mathematics.
- Having encouraged Hausdorff to move to Bonn, Study encouraged him to move again in 1913, this time to become an ordinary professorship at Greifswald.
- A year later, in 1914, Hausdorff published his famous text Grundzüge der Mengenlehre Ⓣ(General set theory) which builds on work by Fréchet and others to created a theory of topological and metric spaces.
- Hausdorff returned to Bonn in 1921, by this time an eminent mathematician, and he worked there until 1935 when he was forced to retire by the Nazi regime.
- Bonn University requested that the Hausdorffs be allowed to remain in their home and this was granted.
- We have mentioned above Hausdorff's early work on astronomy, his work on philosophy, and his literature.
- Let us now examine other important contributions made by Hausdorff.
- In 1919 he introduced the notion of Hausdorff dimension in the seminal paper Dimension und äusseres Mass Ⓣ(Dimension and outer measure).
- The idea was a generalisation of one which had been introduced five years earlier by Carathéodory but Hausdorff realised that Carathéodory's construction made sense, and was useful, for defining fractional dimensions.
- Hausdorff's paper includes a proof that the dimension of the middle-third Cantor set is log 2/log 3.
- It is not well known that throughout his life Hausdorff had been interested in various fundamental problems of measure and integration theory and had made important contributions at different times.
- One such lecture course was given on probability theory by Hausdorff in Bonn in the summer of 1923.

Born 8 November 1868, Breslau, Prussia (now Wrocław, Poland). Died 26 January 1942, Bonn, Germany.

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Analysis, Astronomy, Bourbaki, Geometry, Origin Poland, Topology

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