Hans Hahn (; 27 September 1879 – 24 July 1934) was an

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

who made contributions to

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defi ...

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

, the

calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...

real analysis In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...

, and

order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

. In philosophy he was among the main

logical positivists Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, is a movement in Western philosophy whose central thesis was the verification principle (also known as the verifiability criterion of ...

of the

Vienna Circle The Vienna Circle (german: Wiener Kreis) of Logical Empiricism was a group of elite philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, ch ...

Biography

Born in

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

as the son of a higher government official of the k.k.

Telegraphen-Korrespondenz Bureau The Telegraphen-Korrespondenz Bureau, also referred to by many other names (''Austrian Correspondence'', Österreichische Correspondenz, Kaiserlich und Königlich Telegraphen-Korrespondenz Bureau, K.u.k. Telegraphen-Korrespondenz-Bureau, or Korbur ...

(since 1946 named "Austria Presse Agentur"), in 1898 Hahn became a student at the

Universität Wien The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histo ...

starting with a study of law. In 1899 he switched over to mathematics and spent some time at the universities of

Strasbourg Strasbourg (, , ; german: Straßburg ; gsw, label= Bas Rhin Alsatian, Strossburi , gsw, label= Haut Rhin Alsatian, Strossburig ) is the prefecture and largest city of the Grand Est region of eastern France and the official seat of the ...

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the third-largest city in Germany, after Berlin and ...

and

Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911. General information The ori ...

. 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 Gustav Ritter von Escherich (1 June 1849 – 28 January 1935) was an Austrian mathematician. Biography Born in Mantua, he studied mathematics and physics at the University of Vienna. From 1876 to 1879 he was professor at the University of Graz. ...

. He was appointed to the teaching staff (

Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including ...

) in Vienna in 1905. After 1905/1906 as a stand-in for Otto Stolz at

Innsbruck Innsbruck (; bar, Innschbruck, label=Austro-Bavarian ) is the capital of Tyrol and the fifth-largest city in Austria. On the River Inn, at its junction with the Wipp Valley, which provides access to the Brenner Pass to the south, it had a p ...

and some further years as a

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...

in Vienna, he was nominated in 1909

Professor extraordinarius Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', ...

Czernowitz Chernivtsi ( uk, Чернівці́}, ; ro, Cernăuți, ; see also other names) is a city in the historical region of Bukovina, which is now divided along the borders of Romania and Ukraine, including this city, which is situated on the up ...

, 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

, now in

Bonn The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ru ...

. In 1917 he was nominated a regular

Professor Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professo ...

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. 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 Positivism is an empiricist philosophical theory that holds that all genuine knowledge is either true by definition or positive—meaning ''a posteriori'' facts derived by reason and logic from sensory experience.John J. Macionis, Linda M. G ...

with Otto Neurath (who had married Hahn’s sister

Olga Hahn-Neurath Olga Hahn-Neurath (; 20 July 1882 – 20 July 1937) was an Austrian mathematician and philosopher. She is best known for being a member of the Vienna Circle. She was sister of the mathematician Hans Hahn. Biography Born in Vienna, Hahn enrolled a ...

in 1912), and Phillip Frank prior to the

First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

. In 1922, he helped arrange

Moritz Schlick Friedrich Albert Moritz Schlick (; ; 14 April 1882 – 22 June 1936) was a German philosopher, physicist, and the founding father of logical positivism and the Vienna Circle. Early life and works Schlick was born in Berlin to a wealthy Prussian f ...

's entry into the group, which led to the founding of the

, the group that was at the center of logical positivist thought in the 1920s. His most famous student was

Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imm ...

, whose Ph.D. thesis was completed in 1929. After

Anschluss The (, or , ), also known as the (, en, Annexation of Austria), was the annexation of the Federal State of Austria into the German Reich on 13 March 1938. The idea of an (a united Austria and Germany that would form a " Greater Germa ...

the fact that Hans Hahn had been of partial Jewish origin caused Gödel's difficulties with getting a position at The University of Vienna. Within the Vienna Circle, Hahn was also known (and controversial) for using his mathematical and philosophical work to study

psychic phenomena A psychic is a person who claims to use extrasensory perception (ESP) to identify information hidden from the normal senses, particularly involving telepathy or clairvoyance, or who performs acts that are apparently inexplicable by natural l ...

; according to

Karl Menger Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician, the son of the economist Carl Menger. In mathematics, Menger studied the theory of algebras and the dimension theory of low- regularity ("rough") curves ...

he sometimes openly advocated further research into

extrasensory perception Extrasensory perception or ESP, also called sixth sense, is a claimed paranormal ability pertaining to reception of information not gained through the recognized physical senses, but sensed with the mind. The term was adopted by Duke Universit ...

while lecturing. Politically Hahn was a socialist and was chairman of the Association of Socialist University Teachers. Hahn's contributions to mathematics include the

Hahn–Banach theorem The Hahn–Banach theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear f ...

and (independently of Banach and

Steinhaus Steinhaus may refer to: *Bibiana Steinhaus, German football referee * Edward Arthur Steinhaus (1914–1969), American insect pathologist * Hugo Steinhaus, mathematician * Steinhaus, Austria, a municipality in Upper Austria, Austria * Steinhaus, ...

) the

uniform boundedness principle In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the corner ...

. Other theorems include: * the Hahn decomposition theorem; * the

Hahn embedding theorem In mathematics, especially in the area of abstract algebra dealing with ordered structures on abelian groups, the Hahn embedding theorem gives a simple description of all linearly ordered abelian groups. It is named after Hans Hahn. Overview T ...

; * the Hahn–Kolmogorov theorem; * the Hahn–Mazurkiewicz theorem; * the Vitali–Hahn–Saks theorem. Hahn authored the book : according to

Arthur Rosenthal Arthur Rosenthal (24 February 1887, Fürth, Germany – 15 September 1959, Lafayette, Indiana) was a German mathematician. Career Rosenthal's mathematical studies started in 1905 in Munich, under Ferdinand Lindemann and Arnold Sommerfeld at the ...

, "''... (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'', 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 The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Math ...

. In 1928 he was an Invited Speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

in Bologna.

Publications

All his mathematical and philosophical works, except all books and all but one of his book reviews, are published in the three volumes , and of his "''Collected papers''". * (freely available at the

Internet Archive The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...

). * * * *. *.

Notes

External links

* * {{DEFAULTSORT:Hahn, Hans 1879 births 1934 deaths Austrian Jews Scientists from Vienna 20th-century Austrian mathematicians Vienna Circle Topologists Set theorists Austrian agnostics Austrian socialists Jewish agnostics Jewish scientists Austro-Hungarian mathematicians Chernivtsi University academic personnel

Biography

Publications

See also

Notes

External links