Editing Felix Hausdorff (section)

==Life==

===Childhood and youth===
Hausdorff's father, the [[Jewish]] merchant Louis Hausdorff (1843–1896), moved with his young family to [[Leipzig]] in the autumn of 1870, and over time worked at various companies, including a linen-and cotton goods factory. He was an educated man and had become a [[Morenu]] at the age of 14. He wrote several treatises, including a long work on the [[Aramaic]] translations of the Bible from the perspective of [[Talmud]]ic law.

Hausdorff's mother, Hedwig (1848–1902), who is also referred to in various documents as Johanna, came from the Jewish Tietz family. From another branch of this family came [[Hermann Tietz]], founder of the first department store, and later co-owner of the department store chain called "Hermann Tietz". During the period of Nazi dictatorship the name was "Aryanised" to [[Hertie]].

From 1878 to 1887 Felix Hausdorff attended the Nicolai School in Leipzig, a facility that had a reputation as a hotbed of humanistic education. He was an excellent student, class leader for many years and often recited self-written Latin or German poems at school celebrations.

In his later years of high school, choosing a main subject of study was not easy for Hausdorff. Magda Dierkesmann, who was often a guest in the home of Hausdorff in the years 1926–1932, reported in 1967 that:

{{blockquote|His versatile musical talent was so great that only the insistence of his father made him give up his plan to study music and become a composer.}}

He decided to study the natural sciences, and in his graduating class of 1887 he was the only one who achieved the highest possible grade.

===Degree, doctorate and Habilitation===

From 1887 to 1891 Hausdorff studied [[mathematics]] and [[astronom]]y, mainly in his native city of Leipzig, interrupted by one semester in [[Freiburg]] (summer 1888) and [[Berlin]] (winter 1888/1889). Surviving testimony from other students depict him as an extremely versatile and interested young man, who, in addition to the mathematical and astronomical lectures, attended lectures in [[physics]], [[chemistry]] and [[geography]], and also lectures on [[philosophy]] and [[history of philosophy]], as well as on issues of [[linguistics|language]], [[literature]] and [[social sciences]]. In Leipzig he attended lectures on the [[history of music]] from musicologist [[Oscar Paul]]. His early love of music lasted a lifetime; in Hausdorff's home he held impressive musical evenings with the landlord at the piano, according to witness statements made by various participants. Even as a student in Leipzig, he was an admirer and connoisseur of the music of [[Richard Wagner]].

In later semesters of his studies, Hausdorff was close to [[Heinrich Bruns]] (1848–1919). 
Bruns was professor of astronomy and director of the observatory at the University of Leipzig. Under his supervision, Hausdorff graduated in 1891 with a work on the theory of astronomical refraction of light in the atmosphere. Two publications on the same subject followed, and in 1895 his [[Habilitation]] also followed with a thesis on the absorbance of light in the atmosphere. These early astronomical works of Hausdorff, despite their excellent mathematical formulation, were ultimately of little importance to the scientific community.
For one, the underlying idea of Bruns was later shown to not be viable (there was a need for refraction observations near the astronomical horizon, and as Julius Bauschinger would show, this could not be obtained with the required accuracy). And further, the progress in the direct measurement of atmospheric data (from [[weather balloon]] ascents) has since made the painstaking accuracy of this data from refraction observations unnecessary. In the time between defending his PhD and his Habilitation, Hausdorff completed his yearlong military requirement, and worked for two years as a [[human computer]] at the [[observatory]] in Leipzig.

===Lecturer in Leipzig===
After his Habilitation, Hausdorff became a lecturer at the University of Leipzig where he began extensive teaching in a variety of mathematical areas. In addition to teaching and research in mathematics, he also pursued his literary and philosophical inclinations. A man of varied interests, he often associated with a number of famous writers, artists and publishers such as [[Hermann Conradi]], [[Richard Dehmel]], [[Otto Erich Hartleben]], [[Gustav Kirstein]], [[Max Klinger]], [[Max Reger]] and [[Frank Wedekind]]. The years of 1897 to 1904 mark the high point of his literary and philosophical creativity, during which time 18 of his 22 pseudonymous works were published, including a book of poetry, a play, an epistemological book and a volume of [[aphorism]]s.

In 1899 Hausdorff married Charlotte Goldschmidt, the daughter of Jewish doctor Siegismund Goldschmidt. Her stepmother was the famous suffragist and preschool teacher [[Henriette Goldschmidt]]. Hausdorff's only child, his daughter Lenore (Nora), was born in 1900; she survived the era of National Socialism and enjoyed a long life, dying in Bonn in 1991.

===First professorship===
In December 1901 Hausdorff was appointed as adjunct associate professor at the University of Leipzig. An often-repeated [[factoid]], that Hausdorff got a call from [[Göttingen]] and rejected it, cannot be verified and is most likely wrong. After considering Hausdorff's application to Leipzig, the Dean Kirchner felt compelled to make the following addition to the very positive vote from his colleagues, written by Heinrich Bruns:

{{blockquote|The faculty, however, considers itself obliged to report to the Royal Ministry that the above application, considered on November 2nd of this year when a faculty meeting had taken place, was not accepted by all, but with 22 votes to 7. The minority was opposed, because Dr. Hausdorff is of the Mosaic faith.<ref>Archiv der Universität Leipzig, PA 547</ref>}}

This quote emphasizes the undisguised [[anti-Semitism|antisemitism]] present, which especially took a sharp upturn throughout the German Reich after the [[Gründerkrach|stock market crash of 1873]]. Leipzig was a focus of antisemitic sentiment, especially among the student body, which may well be the reason that Hausdorff did not feel at ease in Leipzig. Another contributing factor may also have been the stresses due to the hierarchical posturing of the Leipzig professors.

After his Habilitation, Hausdorff wrote other works on [[optics]], on [[non-Euclidean geometry]], and on [[hypercomplex number]] systems, as well as two papers on [[probability theory]]. However, his main area of work soon became set theory, especially the theory of [[ordered set]]s. Initially, it was only out of philosophical interest that Hausdorff began to study [[Georg Cantor]]'s work, beginning around 1897, but already in 1901 Hausdorff began lecturing on set theory. His was one of the first ever lectures on set theory; only [[Ernst Zermelo]]'s lectures in Göttingen College during the winter of 1900/1901 were earlier. That same year, he published his first paper on order types in which he examined a generalization of [[well-ordering]]s called [[graded order types]], where a [[linear order]] is graded if no two of its segments share the same [[order type]]. He generalized the [[Cantor–Bernstein theorem]], which said the collection of countable order types has the [[cardinality of the continuum]] and showed that the collection of all graded types of an [[Idempotence|idempotent]] cardinality {{var|m}} has a cardinality of 2<sup>{{var|m}}</sup>.<ref>{{Cite book|title = Handbook of the History of Logic: Sets and extensions in the twentieth century|url = https://books.google.com/books?id=ZF_QckMFy-oC&q=graded%2520order%2520type&pg=PA159|publisher = Elsevier|date = 2012-01-01|isbn = 9780444516213|language = en|first = Dov M.|last = Gabbay}}</ref>

For the summer semester of 1910 Hausdorff was appointed as professor to the [[University of Bonn]]. There he began a lecture series on set theory, which he substantially revised and expanded for the summer semester of 1912.

In the summer of 1912 he also began work on his magnum opus, the book ''Basics of set theory''. It was completed in [[Greifswald]], where Hausdorff had been appointed for the summer semester as full professor in 1913, and was released in April 1914.

The [[University of Greifswald]] was the smallest of the Prussian universities. The mathematical institute there was also small; during the summer of 1916 and the winter of 1916/17, Hausdorff was the only mathematician in Greifswald. This meant that he was almost fully occupied in teaching basic courses. It was thus a substantial improvement for his academic career when Hausdorff was appointed in 1921 to Bonn. There he was free to teach about wider ranges of topics, and often lectured on his latest research. He gave a particularly noteworthy lecture on probability theory (NL Hausdorff: Capsule 21: Fasz 64) in the summer semester of 1923, in which he grounded the theory of probability in measure-theoretic axiomatic theory, ten years before [[Andrey Kolmogorov|A. N. Kolmogorov]]'s "Basic concepts of probability theory" (reprinted in full in the collected works, Volume V). In Bonn, Hausdorff was friends and colleagues with [[Eduard Study]], and later with [[Otto Toeplitz]], who were both
outstanding mathematicians.

===Under the Nazi dictatorship and suicide===
After the takeover by the [[National Socialist]] party, [[anti-Semitism|antisemitism]] became state doctrine. Hausdorff was not initially concerned by the "[[Law for the Restoration of the Professional Civil Service]]", adopted in 1933, because he had been a German public servant since before 1914. However, he was not completely spared, as one of his lectures was interrupted by National Socialist student officials. In the winter semester of 1934/1935, there was a working session of the National Socialist German Student Union (NSDStB) at the University of Bonn, which chose "Race and Ethnicity" as their theme for the semester. Hausdorff cancelled his 1934/1935 winter semester Calculus III course on 20 November, and it is assumed that the choice of theme was related to the cancellation of Hausdorff's class, since in his long career as a university lecturer he had always taught his courses through to their end.

On March 31, 1935, after some back and forth, Hausdorff was finally given emeritus status. No words of thanks were given for his 40 years of successful work in the German higher education system.

His [[Nachlass|academic legacy]] shows that Hausdorff was still working mathematically during these increasingly difficult times, and continued to follow current developments of interest. 
He wrote, in addition to the expanded edition of his work on set theory, seven works on topology and descriptive set theory. These were published in Polish magazines: one in ''[[Studia Mathematica]]'', the others in ''[[Fundamenta Mathematicae]]''.
He was supported at this time by [[Erich Bessel-Hagen]], a loyal friend to the Hausdorff family who obtained books and magazines from the academic library, which Hausdorff was no longer allowed to enter.

A great deal is known about the humiliations to which Hausdorff and his family especially were exposed to after [[Kristallnacht]] in 1938. There are many sources, including the letters of Bessel-Hagen.<ref>Neuenschwander, E.: ''Felix Hausdorffs letzte Lebensjahre nach Dokumenten aus dem Bessel-Hagen-Nachlaß''. In: Brieskorn 1996, S.&nbsp;253–270.</ref>

[[File:Abschiedsbrief Felix Hausdorffs – Seite 1.png|thumb|The first page of his farewell letter to Hans Wollstein]]

In 1939, Hausdorff asked the mathematician [[Richard Courant]], in vain, for a research fellowship to be able to emigrate into the USA. 
In mid-1941, the Bonn Jews began to be deported to the "Monastery for Eternal Adoration" in [[Endenich]], [[Bonn]], from which the nuns had been expelled. Transports to death camps in the east occurred later. After Hausdorff, his wife, and his wife's sister, Edith Pappenheim (who was living with them), were ordered in January 1942 to move to the Endenich camp, the three died by suicide on 26 January 1942 by taking an overdose of [[veronal]].<ref>Schubring, G. (2021). Biographie. Felix Hausdorff, Gesammelte Werke. Band IB. by Egbert Brieskorn and Walter Purkert. Math Intelligencer 43, 94–98</ref> Their final resting place is located on the cemetery [[Poppelsdorf]] in Bonn. In the time between their placement in temporary camps and his suicide, he gave his handwritten ''[[Nachlass]]'' to the Egyptologist and presbyter [[Hans Bonnet]], who saved as much of them as possible, even despite the destruction of his house by a bomb.

Some of his fellow Jews may have had illusions about the camp Endenich, but not Hausdorff. In the estate of Bessel-Hagen, E. Neuenschwander discovered the farewell letter that Hausdorff wrote to his lawyer Hans Wollstein, who was also Jewish.<ref>Nachlass Bessel-Hagen, Universitätsarchiv Bonn. Abgedruckt in Brieskorn 1996, S.&nbsp;263–264 und im Faksimile S.&nbsp;265–267</ref><ref>{{Wikisource-inline|de:Abschiedsbrief Felix Hausdorffs|Abschiedsbrief Felix Hausdorffs|single=true}}</ref> Here is the beginning and end of the letter:

[[File:Hausdorff-Grab.jpg|thumb|Hausdorff's gravestone in Bonn-[[Poppelsdorf]]]]

{{blockquote|Dear friend Wollstein!

If you receive these lines, we (three) have solved the problem in a different manner — in the manner of which you have constantly tried to dissuade us. The feeling of security that you have predicted for us once we would overcome the difficulties of the move, is still eluding us; on the contrary, Endenich may not even be the end!

What has happened in recent months against the Jews evokes justified fear that they will not let us live to see a more bearable situation.}}

After thanking friends and, in great composure, expressing his last wishes regarding his funeral and his will, Hausdorff writes:

{{blockquote|I am sorry that we cause you yet more effort beyond death, and I am convinced that you are doing what you <u>can</u> do (which perhaps is not very much). Forgive us our desertion! We wish you and all our friends to experience better times.

Your truly devoted

Felix Hausdorff}}

Unfortunately, this desire was not fulfilled. Hausdorff's lawyer, Wollstein, was murdered in [[Auschwitz]].

[[File:Hausdorff-strasse.jpg|thumb|Hausdorffstraße (Bonn)]]

Hausdorff's library was sold by his son-in-law and sole heir, Arthur König. The portions of Hausdorff's ''[[Nachlass]]'' which could be saved by Hans Bonnet are now in the university and State Library of Bonn. The ''Nachlass'' is catalogued.<ref>Siehe Findbuch Nachlass Hausdorff</ref>