Hans Hahn (mathematician)

{{Infobox scientist

| name = Hans Hahn

| image = Hans Hahn.jpg

| image_size = 200px

| caption = Hans Hahn (about 1905)

| birth_date = {{birth date|1879|9|27|df=y}}

| birth_place = Vienna, Austria-Hungary

| death_date = {{death date and age|1934|7|24|1879|9|27|df=y}}

| death_place = Vienna, Austria

| field = {{plainlist|

| work_institutions = {{plainlist|

| education = University of Vienna (PhD, 1902)

| thesis_title = Zur Theorie der zweiten Variation einfacher Integrale

| thesis_url =

| thesis_year = 1902

| doctoral_advisor = Gustav Ritter von Escherich

| doctoral_students = {{plainlist|

| notable_students = Karl Popper

| known_for = {{plainlist|

| prizes = Lieben Prize (1921)

}}

Hans Hahn ({{IPAc-en|h|ɑː|n}}; {{IPA|de|haːn|lang}}; 27 September 1879 – 24 July 1934) was an Austrian mathematician and philosopher who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. In philosophy he was among the main logical positivists of the Vienna Circle.

Biography

Born in Vienna as the son of a higher government official of the K.K. Telegraphen-Korrespondenz Bureau (since 1946 named "Austria Presse Agentur"), in 1898 Hahn became a student at the Universität Wien starting with a study of law. In 1899 he switched over to mathematics and spent some time at the universities of Strasbourg, Munich and Göttingen. In 1902 he took his Ph.D. in Vienna, on the subject "Zur Theorie der zweiten Variation einfacher Integrale". He was a student of Gustav von Escherich.

He was appointed to the teaching staff (Habilitation) in Vienna in 1905. After 1905/1906 as a stand-in for Otto Stolz at the University of Innsbruck and some further years as a Privatdozent in Vienna, he was nominated in 1909 Professor extraordinarius in Czernowitz, at that time a town within the empire of Austria. After joining the Austrian army in 1915, he was badly wounded in 1916 and became again Professor extraordinarius, now in Bonn. In 1917 he was nominated a regular Professor there and in 1921 he returned to Vienna with this title, where he stayed until his rather early death in 1934 at the age of 54, following cancer surgery.{{cite book|last1=Hans|first1=Hahn|title=Hans Hahn Collected Works Volume 1|date=Mar 7, 2013|publisher=Springer Verlag|isbn=9783709166017|pages=28}}

He had married Eleonore ("Lilly") Minor in 1909 and they had a daughter, Nora (born 1910).

He was also interested in philosophy, and was part of a discussion group concerning Mach's positivism with Otto Neurath (who had married Hahn’s sister Olga Hahn-Neurath in 1912), and Phillip Frank prior to the First World War. In 1922, he helped arrange Moritz Schlick's entry into the group, which led to the founding of the Vienna Circle, the group that was at the center of logical positivist thought in the 1920s. His most famous student was Kurt Gödel, whose Ph.D. thesis was completed in 1929. After Anschluss the fact that Hans Hahn had been of partial Jewish originDan Diner (Ed.), Enzyklopädie jüdischer Geschichte und Kultur: Band 6: Te–Z, p. 403, Springer-Verlag, 2017 caused Gödel's difficulties with getting a position at the University of Vienna.Richard Tieszen, Simply Gödel, Simply Charly, New York, 2017. Within the Vienna Circle, Hahn was also known (and controversial) for using his mathematical and philosophical work to study psychic phenomena; according to Karl Menger he sometimes openly advocated further research into extrasensory perception while lecturing.{{Cite book | last = Josephson-Storm | first = Jason | title = The Myth of Disenchantment: Magic, Modernity, and the Birth of the Human Sciences | location = Chicago | publisher = University of Chicago Press | date = 2017 |pages = 260–3 | url = https://books.google.com/books?id=xZ5yDgAAQBAJ | isbn = 978-0-226-40336-6 }}

Politically Hahn was a socialist and was chairman of the Association of Socialist University Teachers.{{cite book |last1=Edmonds |first1=David |title=The Murder of Professor Schlick: The Rise and Fall of the Vienna Circle |publisher=Princeton University Press |page=134}} He contributed to the Social Democrat magazine Der Kampf.{{cite book |last1=Edmonds |first1=David |title=The Murder of Professor Schlick: The Rise and Fall of the Vienna Circle |date=2020 |publisher=Princeton University Press |location=Princeton |isbn=9780691164908 |page=136 |edition=First}}

Hahn's contributions to mathematics include the Hahn–Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. Other theorems include:

Hahn authored the book {{harv|Hahn|1921}}: according to Arthur Rosenthal,See Arthur Rosenthal preface to the book {{harv|Hahn|Rosenthal|1948|p=v}}. "... (it) formed a great advance in the Theory of Real functions and had a great influence on the further development of this theory". He was also a co-author of the book Set Functions,See {{harv|Hahn|Rosenthal|1948}}. published in 1948 by Arthur Rosenthal, fourteen years after his death in Vienna in 1934.

In 1921 he received the Richard Lieben Prize. In 1926 he was the president of the German Mathematical Society. In 1928 he was an Invited Speaker at the International Congress of Mathematicians in Bologna.Hahn, H. "Über stetige Streckenbilder". In Atti del Congresso internazionale dei Matematici, Bologna, 1928, vol. 2, pp. 217–220; reprinted in: Hahn H. (1995) "Über stetige Streckenbilder". In: Schmetterer L., Sigmund K. (eds) Hans Hahn Gesammelte Abhandlungen Band 1/Hans Hahn Collected Works Volume 1, pp. 435–438. Springer, Vienna {{doi|10.1007/978-3-7091-6601-7_16}}

Hahn died in 1934 following surgery for a newly diagnosed cancer. He was only 54 and his death came as a shock to friends and colleagues.Brewer, William D. "Kurt Gödel: The Genius of Metamathematics." Springer Nature. 2022. Page 177.

Publications

All his mathematical and philosophical works, except all books and all but one of his book reviews, are published in the three volumes {{harv|Hahn|1995}}, {{harv|Hahn|1996}} and {{harv|Hahn|1997}} of his "Collected papers".According to S.Gottwald in his review {{Zbl|0859.01030}} of the first volume {{harv|Hahn|1995}}.

{{Citation

| last = Hahn

| first = Hans

| author-link =

| title = Theorie der reellen Funktionen. Erster Band

| place =Berlin–Heidelberg

| publisher =Springer-Verlag

| year =1921

| pages =VII+600

| language =German

| url = https://archive.org/details/theoriederreell00hahngoog

| doi =10.1007/978-3-642-52624-4

| id =

| isbn =978-3-642-52570-4

| jfm = 48.0261.09

| hdl =2027/pst.000003378601

| hdl-access =free

}}{{cite journal|author=Jackson, Dunham|authorlink=Dunham Jackson|title=Review: Theorie der reellen Funktionen, by Hans Hahn|journal=Bull. Amer. Math. Soc.|year=1922|volume=28|issue=8|pages=408–411|url=https://www.ams.org/journals/bull/1922-28-08/S0002-9904-1922-03604-X/S0002-9904-1922-03604-X.pdf|doi=10.1090/s0002-9904-1922-03604-x|doi-access=free}} (freely available at the Internet Archive).

{{Citation

| last = Hahn

| first = Hans

| author-link =

| title = Reelle Funktionen. Tl. 1. Punktfunktionen

| place =Leipzig

| publisher =Akademische Verlagsgesellschaft

| series=Mathematik und ihre Anwendungen in Monographien und Lehrbüchern

| volume= Band 13

| year =1932

| pages =XII+415

| language =German

| url =

| doi =

| id =

| isbn =

| jfm = 58.0242.05

| zbl = 0005.38903

}}{{cite journal|author=Whyburn, G. T.|authorlink=Gordon Thomas Whyburn|title=Review: Reelle Funktionen. Erste Teil: Punktfunktionen, by Hans Hahn|journal=Bull. Amer. Math. Soc.|year=1933|volume=39|issue=9|pages=655|url=https://www.ams.org/journals/bull/1933-39-09/S0002-9904-1933-05702-6/S0002-9904-1933-05702-6.pdf|doi=10.1090/s0002-9904-1933-05702-6|doi-access=free}}

{{Citation

| last1=Hahn

| first1=Hans

| last2=Rosenthal

| first2=Arthur

| author2-link=Arthur Rosenthal

| title=Set Functions

| place =Albuquerque, N. M.

| publisher=The University of New Mexico Press

| year=1948

| pages=ix+324

| mr=0024504

| zbl=0033.05301

}}{{cite journal|author=Federer, Herbert|authorlink=Herbert Federer|title=Review: Set Functions, by Hans Hahn and Arthur Rosenthal|journal=Bull. Amer. Math. Soc.|year=1949|volume=55|issue=3|pages=316–317|url=https://www.ams.org/journals/bull/1949-55-03/S0002-9904-1949-09195-4/S0002-9904-1949-09195-4.pdf|doi=10.1090/s0002-9904-1949-09195-4}}