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Quick facts for kids Felix Hausdorff

Born	(1868-11-08)November 8, 1868 Breslau, Kingdom of Prussia (now Wrocław, Poland)
Died	January 26, 1942(1942-01-26) (aged 73) Bonn, Germany
Nationality	German
Alma mater	University of Leipzig
Known for	η set Back-and-forth method Baker–Campbell–Hausdorff formula Hausdorff completion Hausdorff dimension Hausdorff distance Hausdorff gap Hausdorff maximal principle Hausdorff measure Hausdorff paradox Hausdorff space Hausdorff moment problem Hausdorff–Young inequality
Spouse(s)	Charlotte Hausdorff (1873-1942)
Scientific career
Fields	Mathematics
Institutions	University of Bonn, University of Greifswald, University of Leipzig
Thesis	Zur Theorie der astronomischen Strahlenbrechung (1891)
Doctoral advisor	Heinrich Bruns Adolph Mayer

Felix Hausdorff (/ˈhaʊsdɔːrf/ HOWS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré, who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, and functional analysis.

Life became difficult for Hausdorff and his family after Kristallnacht in 1938. The next year he initiated efforts to emigrate to the United States, but was unable to make arrangements to receive a research fellowship. .....

Life
Hausdorff as name-giver
Writings
- As Paul Mongré
- As Felix Hausdorff
Collected works
See also

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 Talmudic 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.

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 astronomy, 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 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 aphorisms.

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.

This quote emphasizes the undisguised antisemitism present, which especially took a sharp upturn throughout the German Reich after the 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 sets. 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-orderings 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 idempotent cardinality m has a cardinality of 2^m.

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 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.

Hausdorff as name-giver

The name Hausdorff is found throughout mathematics. Among others, these concepts were named after him:

Hausdorff completion
Hausdorff convergence
Hausdorff density
Hausdorff dimension
Hausdorff distance
Hausdorff gap
Hausdorff maximal principle
Hausdorff measure
Hausdorff metric
Hausdorff moment problem
Hausdorff paradox
Hausdorff space
Hausdorff–Young inequality
Baker–Campbell–Hausdorff formula

In the universities of Bonn and Greifswald, these things were named in his honor:

the Hausdorff Center for Mathematics in Bonn,
the Hausdorff Research Institute for Mathematics in Bonn, and
the Felix Hausdorff Internationale Begegnungszentrum in Greifswald.

Besides these, in Bonn there is the Hausdorffstraße (Hausdorff Street), where he first lived. (Haus-Nr. 61). In Greifswald there is a Felix-Hausdorff–Straße, where the Institutes for Biochemistry and Physics are located, among others. Since 2011, there is a "Hausdorffweg" (Hausdorff-Way) in the middle of Leipziger Ortsteil Gohlis.

The Asteroid 24947 Hausdorff was named after him.

Writings

As Paul Mongré

Only a selection of the essays that appeared in text are shown here.

Sant'Ilario. Gedanken aus der Landschaft Zarathustras. Verlag C. G. Naumann, Leipzig 1897.
Das Chaos in kosmischer Auslese — Ein erkenntniskritischer Versuch. Verlag C. G. Naumann, Leipzig 1898; Reprinted with foreword by Max Bense: Baden-Baden: Agis-Verlag 1976, ISBN: 3-87007-013-7
Massenglück und Einzelglück. Neue Deutsche Rundschau (Freie Bühne) 9 (1), (1898), S. 64–75.
Das unreinliche Jahrhundert. Neue Deutsche Rundschau (Freie Bühne) 9 (5), (1898), S. 443–452.
Ekstasen. Volume of poetry. Verlag H. Seemann Nachf., Leipzig 1900.
Der Wille zur Macht. In: Neue Deutsche Rundschau (Freie Bühne) 13 (12) (1902), S. 1334–1338.
Max Klingers Beethoven. Zeitschrift für bildende Kunst, Neue Folge 13 (1902), S. 183–189.
Sprachkritik Neue Deutsche Rundschau (Freie Bühne) 14 (12), (1903), S. 1233–1258.
Der Arzt seiner Ehre, Groteske. In: Die neue Rundschau (Freie Bühne) 15 (8), (1904), S. 989-1013. New edition as: Der Arzt seiner Ehre. Komödie in einem Akt mit einem Epilog. With 7 portraits and woodcuts by Hans Alexander Müller after drawings by Walter Tiemann, 10 Bl., 71 S. Fifth printing by Leipziger Bibliophilen-Abends, Leipzig 1910. New edition: S. Fischer, Berlin 1912, 88 S.

As Felix Hausdorff

Beiträge zur Wahrscheinlichkeitsrechnung. Proceedings of the Royal Saxon Society for the Sciences at Leipzig. Math.-phys. Classe 53 (1901), S. 152–178.
Über eine gewisse Art geordneter Mengen. Proceedings of the Royal Saxon Society for the Sciences at Leipzig. Math.-phys. Classe 53 (1901), S. 460–475.
Das Raumproblem (Inaugural lecture at the University of Leipzig on 4. July 1903). Ostwald's Annals of Natural Philosophy 3 (1903), S. 1–23.
Der Potenzbegriff in der Mengenlehre. Annual report of the DMV 13 (1904), S. 569–571.
Untersuchungen über Ordnungstypen I, II, III. Proceedings of the Royal Saxon Society for the Sciences at Leipzig. Math.-phys.\ Klasse 58 (1906), S. 106–169.
Untersuchungen über Ordnungstypen IV, V. Proceedings of the Royal Saxon Society for the Sciences at Leipzig. Math.-phys. Klasse 59 (1907), S. 84–159.
Über dichte Ordnungstypen. Annual report of the DMV 16 (1907), S. 541–546.
Grundzüge einer Theorie der geordneten Mengen. Math. Annalen 65 (1908), S. 435–505.
Die Graduierung nach dem Endverlauf. Proceedings of the Royal Saxon Society for the Sciences at Leipzig. Math.-phys. Klasse 31 (1909), S. 295–334.
Grundzüge der Mengenlehre. Verlag Veit & Co, Leipzig. 476 S. mit 53 Figuren. Further printings: Chelsea Pub. Co. 1949, 1965, 1978.
Die Mächtigkeit der Borelschen Mengen. Math. Annalen 77 (1916), S. 430–437.
Dimension und äußeres Maß. Math. Annalen 79 (1919), S. 157–179.
Über halbstetige Funktionen und deren Verallgemeinerung. Math. Zeitschrift 5 (1919), S. 292–309.
Summationsmethoden und Momentfolgen I, II. Math. Zeitschrift 9 (1921), I: S. 74-109, II: S. 280–299.
Eine Ausdehnung des Parsevalschen Satzes über Fourierreihen. Math. Zeitschrift 16 (1923), S. 163–169.
Momentprobleme für ein endliches Intervall. Math. Zeitschrift 16 (1923), S. 220–248.
Mengenlehre, second reworked edition. Verlag Walter de Gruyter & Co., Berlin. 285 S. with 12 figures.
Erweiterung einer Homöomorphie (PDF; 389 kB) Fundamenta Mathematicae 16 (1930), S. 353–360.
Mengenlehre, third edition. With an additional chapter and several appendices. Verlag Walter de Gruyter & Co., Berlin. 307 S. mit 12 Figuren. Nachdruck: Dover Pub. New York, 1944. Englisch edition: Set theory. Translated from the German by J. R. Aumann et al. Chelsea Pub. Co., New York 1957, 1962, 1967.
Gestufte Räume. (PDF; 1,2 MB) Fundamenta Mathematicae 25 (1935), S. 486–502.
Erweiterung einer stetigen Abbildung (PDF; 450 kB) Fundamenta Mathematicae 30 (1938), S. 40–47.
Nachgelassene Schriften. 2 volumes. Ed.: G. Bergmann, Teubner, Stuttgart 1969. From the Nachlass, Volume I includes fascicles 510–543, 545–559, 561–577, Volume II fascicles 578–584, 598–658 (all fascicles given in facsimile).

Hausdorff on Ordered Sets. Trans. and Ed.: Jacob M. Plotkin, American Mathematical Society 2005.

Collected works

The "Hausdorff-Edition", edited by E. Brieskorn (†), F. Hirzebruch (†), W. Purkert (all Bonn), R. Remmert (†) (Münster) and E. Scholz (Wuppertal) with the collaboration of over twenty mathematicians, historians, philosophers and scholars, is an ongoing project of the North Rhine-Westphalian Academy of Sciences, Humanities and the Arts to present the works of Hausdorff, with commentary and much additional material. The volumes have been published by Springer-Verlag, Heidelberg. Nine volumes have been published with volume I being split up into volume IA and volume IB. See the website of the Hausdorff Project website of the Hausdorff Edition (German) for further information. The volumes are:

Band IA: Allgemeine Mengenlehre. 2013, ISBN: 978-3-642-25598-4.
Band IB: Felix Hausdorff – Paul Mongré (Biographie). 2018, ISBN: 978-3-662-56380-9.
Band II: Grundzüge der Mengenlehre (1914). 2002, ISBN: 978-3-540-42224-2
Band III: Mengenlehre (1927, 1935); Deskriptive Mengenlehre und Topologie. 2008, ISBN: 978-3-540-76806-7
Band IV: Analysis, Algebra und Zahlentheorie. 2001, ISBN: 978-3-540-41760-6
Band V: Astronomie, Optik und Wahrscheinlichkeitstheorie. 2006, ISBN: 978-3-540-30624-5
Band VI: Geometrie, Raum und Zeit. 2020. ISBN: 978-3-540-77838-7
Band VII: Philosophisches Werk. 2004, ISBN: 978-3-540-20836-5
Band VIII: Literarisches Werk. 2010, ISBN: 978-3-540-77758-8
Band IX: Korrespondenz. 2012, ISBN: 978-3-642-01116-0.