Editing Hugo Steinhaus

{{Short description|Polish mathematician (1887–1972)}}
{{Good article}}
{{Infobox scientist
| name              = Hugo Steinhaus
| image             = Hugo Steinhaus.jpg
| image_size        = 200px
| caption           = Hugo Steinhaus (1968)
| birth_name        = Hugo Dyonizy Steinhaus
| birth_date        = {{birth date|1887|1|14|df=y}}
| birth_place       = [[Jasło]], [[Austria-Hungary]] (now Poland)
| death_date        = {{death date and age|1972|2|25|1887|1|14|df=y}}
| death_place       = [[Wrocław]], [[People's Republic of Poland]]
| nationality       = Polish
<!--| ethnicity = [[History of the Jews in Poland|Jewish]]-->
| field             = [[Mathematician]] and mathematics populariser
| work_institutions = [[Lviv University#Second Polish Republic|Jan Kazimierz University]]<br />[[University of Wrocław]]<br />[[University of Notre Dame]]<br />[[University of Sussex]]
| alma_mater        = [[Lviv University#Austrian rule|Lemberg University]]<br />[[University of Göttingen|Göttingen University]]
| doctoral_advisor  = [[David Hilbert]]
| doctoral_students = [[Stefan Banach]]<br />[[Z. W. Birnbaum|Z. W. (Bill) Birnbaum]]<br />[[Mark Kac]]<br />[[Władysław Orlicz]]<br />[[Aleksander Rajchman]]<br />[[Juliusz Schauder]]<br />[[Stanisław Trybuła|Stanisław Trybula]]
| known_for         = [[Uniform boundedness principle|Banach–Steinhaus theorem]], many others, see [[Hugo Steinhaus#Mathematical contributions|section below]].
| prizes            = [[Polish Mathematical Society#Stefan Banach Prize|Stefan Banach Prize]] (1946)
}}

'''Hugo Dyonizy Steinhaus''' ({{IPAc-en|lang|ˈ|h|j|uː|ɡ|oʊ|_|ˈ|s|t|aɪ|n|h|aʊ|s}} {{respell|HEW|goh|_|STYNE|howss}}; {{IPA|pl|ˈxuɡɔ ˈʂtajnxaws|lang}}; {{IPA|de|ˈhuːɡoː ˈʃtaɪnhaʊs|lang}}; 14 January 1887 – 25 February 1972) was a Polish [[mathematician]] and [[teacher|educator]]. Steinhaus obtained his PhD under [[David Hilbert]] at [[Göttingen University]] in 1911 and later became a professor at the [[Lviv University#Second Polish Republic|Jan Kazimierz University]] in [[Lwów]] (now Lviv, Ukraine), where he helped establish what later became known as the [[Lwów School of Mathematics]]. He is credited with "discovering" mathematician [[Stefan Banach]], with whom he gave a notable contribution to [[functional analysis]] through the [[Banach–Steinhaus theorem]]. After [[World War II]] Steinhaus played an important part in the establishment of the mathematics department at [[Wrocław University]] and in the revival of Polish mathematics from the destruction of the war.

Author of around 170 scientific articles and books, Steinhaus has left his legacy and contribution in many branches of mathematics, such as functional analysis, [[geometry]], [[mathematical logic]], and [[trigonometry]]. Notably he is regarded as one of the early founders of [[game theory]] and [[probability theory]], which led to later development of more comprehensive approaches by other scholars.

==Early life and studies==
Steinhaus was born on January 14, 1887, in [[Jasło]],<ref name="100y"/> [[Austria-Hungary]] to a family with [[Jewish]] roots. His father, Bogusław, was a local industrialist, owner of a brick factory and a merchant. His mother was Ewelina, née Lipschitz. Hugo's uncle, {{ill|Ignacy Steinhaus|pl}}, was a lawyer and an activist in the ''Koło Polskie'' (Polish Circle), and a deputy to the [[Diet of Galicia|Galician Diet]], the regional [[Legislative Assembly|assembly]] of the [[Kingdom of Galicia and Lodomeria]].<ref name="jaslo"/>
[[File:Polish students in Gottingen.jpg|thumb|left|Steinhaus, standing rightmost, in 1907 in Göttingen]]
Hugo finished his studies at the [[gymnasium (school)|gymnasium]] in Jasło in 1905. His family wanted him to become an [[engineer]] but he was drawn to [[pure mathematics|abstract mathematics]] and began to study the works of famous contemporary mathematicians on his own. In the same year he began studying philosophy and mathematics at the [[Lviv University#Austrian rule|University of Lemberg]].<ref name=jaslo/> In 1906 he transferred to [[University of Göttingen|Göttingen University]].<ref name=100y/> At that University he received his Ph.D. in 1911, having written his doctoral dissertation under the supervision of [[David Hilbert]]. The title of his thesis was ''Neue Anwendungen des Dirichlet'schen Prinzips'' ("New applications to [[Dirichlet's principle]]").<ref name="kac"/>

At the start of [[World War I]] Steinhaus returned to Poland and served in [[Józef Piłsudski]]'s [[Polish Legions in World War I|Polish Legion]], after which he lived in [[Kraków]].<ref name="mac"/>

He was an atheist.<ref>{{cite book|title=Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical|date=2002|publisher=Mathematical Association of America|isbn=9780883855393|page=[https://archive.org/details/mathematicalapoc00stev/page/202 202]|author=Steven G. Krantz|quote=Steinhaus was an outspoken atheist.|url-access=registration|url=https://archive.org/details/mathematicalapoc00stev/page/202}}</ref>

==Academic career==

===Interwar Poland===
During the 1916-1917 period and before Poland had regained its full [[Polish Independence Day|independence]], which occurred in 1918, Steinhaus worked in Kraków for the [[Ministry of Interior and Administration of the Republic of Poland|Ministry of the Interior]] in the ephemeral puppet state of [[Kingdom of Poland (1916–1918)|Kingdom of Poland]].<ref name=uniw/>

In 1917 he started to work at the University of Lemberg (later [[Lviv University#Second Polish Republic|Jan Kazimierz University]] in Poland) and acquired his [[habilitation]] qualification in 1920.<ref name=uniw/> In 1921 he became a ''profesor nadzwyczajny'' ([[associate professor]]) and in 1925 ''profesor zwyczajny'' (full professor) at the same university.<ref name=uniw/> During this time he taught a course on the then cutting edge theory of [[Lebesgue integration]], one of the first such courses offered outside of [[France]].<ref name=kac/>

While in Lwów, Steinhaus co-founded the [[Lwów School of Mathematics]]<ref name=wroc/> and was active in the circle of mathematicians associated with the [[Scottish Café|Scottish cafe]], although, according to [[Stanislaw Ulam]], for the circle's gatherings, Steinhaus would have generally preferred a more upscale tea shop down the street.<ref name=mac/>

===World War II===
[[File:KsiegaSzkocka1.JPG|thumb|left|200px|The [[Scottish Book]] from the [[Lwów School of Mathematics]], which Steinhaus contributed to and probably saved during World War II.]]
In September 1939 after [[Invasion of Poland|Nazi Germany]] and the [[Soviet invasion of Poland|Soviet Union]] both invaded and occupied Poland, as a fulfillment of the [[Molotov–Ribbentrop Pact]] they had signed earlier, Lwów initially came under Soviet occupation. Steinhaus considered escaping to [[Hungary]] but ultimately decided to remain in Lwów. The Soviets reorganized the university to give it a more [[Ukrainians|Ukrainian]] character, but they did appoint [[Stefan Banach]] (Steinhaus's student) as the dean of the mathematics department and Steinhaus resumed teaching there. The faculty of the department at the school were also strengthened by several Polish refugees from German-occupied Poland. According to Steinhaus, during the experience of this period, he "acquired an insurmountable physical disgust in regard to all sorts of Soviet administrators, politicians and commissars"{{Cref2|A}}

During the interwar period and the time of the Soviet occupation, Steinhaus contributed ten problems to the famous ''[[Scottish Book]]'', including the [[Banach's matchbox problem|last one]], recorded shortly before Lwów was captured by the Nazis in 1941, during [[Operation Barbarossa]].<ref name=mac/>

Steinhaus, because of his Jewish background, spent the [[Nazi occupation of Poland|Nazi occupation]] in hiding, first among friends in Lwów, then in the small towns of [[Osiczyna]], near [[Zamość]] and [[Berdechów]], near Kraków.<ref name="wroc"/><ref name="kac2"/> The [[Polish anti-Nazi resistance]] provided him with false documents of a forest ranger who had died sometime earlier, by the name of Grzegorz Krochmalny. Under this name he taught clandestine classes (higher education was [[Education in Poland during World War II|forbidden for Poles under the German occupation]]). Worried about the possibility of imminent death if captured by Germans, Steinhaus, without access to any scholarly material, reconstructed from memory and recorded all the mathematics he knew, in addition to writing other voluminous memoirs, of which only a little part has been published.<ref name=kac2/>

Also while in hiding, and cut off from reliable news on the course of the war, Steinhaus devised a statistical means of estimating for himself the German casualties at the front based on sporadic obituaries published in the local press. The method relied on the relative frequency with which the obituaries stated that the soldier who died was someone's son, someone's "second son", someone's "third son" and so on.<ref name=kac2/>

According to his student and biographer, [[Mark Kac]], Steinhaus told him that the happiest day of his life were the twenty four hours between the time that the Germans left occupied Poland and the Soviets had not yet arrived ("They had left, and they had not yet come").<ref name=kac2/>

===After World War II===
[[File:Steinhaus-tablica.JPG|right|thumb|250px|Commemorative plaque, [[Wrocław]], Poland]]
In the last days of World War II Steinhaus, still in hiding, heard a rumor that University of Lwów was to be transferred to the city of [[Breslau]] ([[Wrocław]]), which Poland was to acquire as a result of the [[Potsdam Agreement]] (Lwów became part of Soviet Ukraine). Although initially he had doubts, he turned down offers for faculty positions in [[Łódź]] and [[Lublin]] and made his way to the city where he began teaching at [[University of Wrocław]].<ref name=wroc/> While there, he revived the idea behind the ''Scottish Book'' from Lwów, where prominent and aspiring mathematicians would write down problems of interest along with prizes to be awarded for their solution, by starting the ''[[New Scottish Book]]''. It was also most likely Steinhaus preserved the original ''Scottish Book'' from Lwów throughout the war and subsequently sent it to Stanisław Ulam, who translated it into English.<ref name=mac/>

With Steinhaus' help, Wrocław University became renowned for mathematics, much as the University of Lwów had been.<ref name=kac2/>

Later, in the 1960s, Steinhaus served as a visiting professor at the [[University of Notre Dame]] (1961–62)<ref name=mac/> and the [[University of Sussex]] (1966).<ref name="wprost"/>

==Mathematical contributions==
{{See also|Banach–Steinhaus theorem|Steinhaus chessboard theorem}}

Steinhaus wrote over 170 works.<ref name=mac/> Unlike his student, Stefan Banach, who tended to specialize narrowly in the field of [[functional analysis]], Steinhaus made contributions to a wide range of mathematical sub-disciplines, including [[geometry]], [[probability theory]], functional analysis, theory of [[Trigonometric series|trigonometric]] and [[Fourier series]] as well as [[mathematical logic]].<ref name=kac/><ref name=mac/> He also wrote in the area of [[applied mathematics]] and enthusiastically collaborated with [[engineers]], [[geologists]], [[economists]], [[physicians]], [[biologists]] and, in Kac's words, "even [[lawyers]]".<ref name=kac2/>

Probably his most notable contribution to [[functional analysis]] was the 1927 proof of the [[Banach–Steinhaus theorem]], given along with Stefan Banach, which is now one of the fundamental tools in this branch of mathematics.

His interest in [[game]]s led him to propose an early formal definition of a [[Strategy (game theory)|strategy]], anticipating [[John von Neumann]]'s more complete treatment of a few years later. Consequently, he is considered an early founder of modern [[game theory]].<ref name=uniw/> As a result of his work on infinite games Steinhaus, together with another of his students, [[Jan Mycielski]], proposed the [[axiom of determinacy]].<ref name=kac2/>

Steinhaus was also an early contributor to, and co-founder of, probability theory, which at the time was in its infancy and not even considered an actual part of mathematics.<ref name=kac2/> He provided the first [[axiom (disambiguation)|axiom]]atic [[measure theory|measure-theoretic]] description of [[coin toss|coin-tossing]], which was to influence the full axiomatization of probability by the Russian mathematician [[Andrey Kolmogorov]] a decade later.<ref name=kac2/> Steinhaus was also the first to offer precise definitions of what it means for two events to be "[[Independence (probability theory)|independent]]", as well as for what it means for a [[random variable]] to be "[[Uniform distribution (continuous)|uniformly distributed]]".<ref name=mac/>

While in hiding during World War II, Steinhaus worked on the fair cake-cutting problem: how to divide a heterogeneous resource among several people with different preferences such that every person believes he received a [[Proportional division|proportional]] share. Steinhaus' work has initiated the modern research of the [[fair cake-cutting]] problem.{{Cref2|B}}

Steinhaus was also the first person to conjecture the [[ham-sandwich theorem]],<ref name=kac2/><ref name= beyer/> and one of the first to propose the method of [[k-means clustering|''k''-means clustering]].<ref name=cluster/>

==Legacy==
Steinhaus is said to have "discovered" the Polish mathematician Stefan Banach in 1916, after he overheard someone utter the words "[[Lebesgue integral]]" while in a Kraków park (Steinhaus referred to Banach as his "greatest mathematical discovery").<ref name="Alfred Tarski: life and logic"/> Together with Banach and the other participant of the park discussion, [[Otto Nikodym]], Steinhaus started the ''Mathematical Society of Kraków'', which later evolved into the [[Polish Mathematical Society]].<ref name=mac/> He was a member of ''PAU'' (the [[Polish Academy of Learning]]) and ''PAN'' (the [[Polish Academy of Sciences]]), ''PTM'' (the [[Polish Mathematical Society]]), the ''Wrocławskie Towarzystwo Naukowe'' ({{ill|Wrocław Scientific Society|pl|Wrocławskie Towarzystwo Naukowe}}) as well as many international scientific societies and science academies.<ref name=uniw/>

Steinhaus also published one of the first articles in ''[[Fundamenta Mathematicae]]'', in 1921.<ref name="One Hundred Volumes of ''Fundamenta Mathematicae''"/> He also co-founded ''[[Studia Mathematica]]'' along with [[Stefan Banach]] (1929),<ref name=wroc/> and  ''Zastosowania matematyki'' (Applications of Mathematics, 1953), ''[[Colloquium Mathematicum]]'', and ''Monografie Matematyczne'' (Mathematical Monographs).<ref name="100y"/>

He received [[Honorary doctorate|honorary doctorate degrees]] from [[Warsaw University]] (1958), [[Wrocław Medical Academy]] (1961), [[Poznań University]] (1963) and Wrocław University (1965).<ref name=wroc2/>

Steinhaus had full command of several foreign languages and was known for his [[aphorism]]s, to the point that a booklet of his most famous ones in [[Polish language|Polish]], [[French language|French]] and [[Latin language|Latin]] has been published posthumously.<ref name=kac2/>

In 2002, the Polish Academy of Sciences and Wrocław University sponsored "2002, The Year of Hugo Steinhaus", to celebrate his contributions to Polish and world science.<ref name=rok/>

Mathematician [[Mark Kac]], Steinhaus's student, wrote:

{{blockquote|"He was one of the architects of the school of mathematics which flowered miraculously in Poland between the two wars and it was he who, perhaps more than any other individual, helped to raise Polish mathematics from the ashes to which it had been reduced by the second World War to the position of new strength and respect which it now occupies. He was a man of great culture and in the best sense of the word a product of Western civilization."<ref name=kac/>}}

==Chief works==
* ''Czym jest, a czym nie jest matematyka'' (What Mathematics Is, and What It Is Not, 1923).<ref name=wroc2/>
* ''Sur le principe de la condensation de la singularités'' (with Banach, 1927)<ref name="kac"/>
* ''Theorie der Orthogonalreihen'' (with [[Stefan Kaczmarz]], 1935).<ref name="kac"/><ref name=ortho/>
* ''Kalejdoskop matematyczny'' (Mathematical Snapshots, 1939).<ref name="kac"/><ref name=wroc2/>
* ''Taksonomia wrocławska'' (A Wroclaw Taxonomy; with others, 1951).<span id="graphs1951"></span>
* ''Sur la liaison et la division des points d'un ensemble fini'' (On uniting and separating the points of a finite set, with others, 1951).<ref name=sur/> One of multiple rediscoveries of [[Borůvka's algorithm]].
* ''Sto zadań'' (One Hundred Problems In Elementary Mathematics, 1964).<ref name=mac/><ref name=100probs/>
* ''Orzeł czy reszka'' (Heads or Tails, 1961).<ref name="Orzel"/>
* ''Słownik racjonalny'' (A Rational Dictionary, 1980).<ref name=slownikr/>

== Family ==
His daughter Lidya Steinhaus was married to [[Jan Kott]].

==See also==
* [[Freiling's axiom of symmetry]]
* [[One-seventh area triangle]]
* [[Johnson–Trotter algorithm]]
* [[Steinhaus conjecture]]
* [[Steinhaus polygon notation]]
* [[Steinhaus theorem]]
* [[Steinhaus longimeter]]
* [[Last diminisher]]

==Notes==
{{Cnote2 Begin|liststyle=upper-alpha}}
{{Cnote2|A|Nabrałem nieprzyzwyciężonej fizycznej wprost odrazy do wszelkich urzędników, polityków i komisarzy sowieckich (Duda, g. 23).}}
{{Cnote2|B|The solution to the two person version of the problem is the classic children's rule [[divide and choose]]. Steinhaus was the first to generalize the problem definition to three or more people, by inviting the [[proportional division]] criterion.}}
{{Cnote2 End}}

==References==
{{reflist|30em|refs=
<ref name="100y">{{cite book |title=Foreword to "One hundred problems in elementary mathematics" |year=1974 |publisher=Courier Dover Publications |isbn= 978-0-486-23875-3|page=4 |url=https://books.google.com/books?id=IARoSNX7hE0C&q=HUgo+Steinhaus+Jaslo&pg=PA4 }}</ref>

<ref name=100probs>{{cite book |title=One hundred problems in elementary mathematics |last=Steinhaus |first=Hugo |year=1974 |publisher=Courier Dover Publications |isbn= 978-0-486-23875-3|url=https://books.google.com/books?id=IARoSNX7hE0C&q=HUgo+Steinhaus+Jaslo&pg=PA4 }}</ref>

<ref name="Alfred Tarski: life and logic">{{cite book |title=Alfred Tarski: life and logic |last1=Feferman |first1=Anita Burdman |author1-link= Anita Burdman Feferman |author2=Feferman, Solomon |author2-link=Solomon Feferman|year=2004 |publisher=Cambridge University Press |isbn=978-0-521-80240-6 |page=29 |url=https://books.google.com/books?id=wqktlxHo9wkC&q=Alfred+Tarski}}</ref>

<ref name="One Hundred Volumes of ''Fundamenta Mathematicae''">{{cite journal |last1=Kuratowski |first1=Kazimierz |last2=Borsuk |first2=Karol |year=1978 |title=One Hundred Volumes of ''Fundamenta Mathematicae'' |journal=[[Fundamenta Mathematicae]] |volume=100 |page=3 |publisher=Polish Academy of Science |url=http://matwbn.icm.edu.pl/ksiazki/fm/fm100/fm100126.pdf }}</ref>

<ref name=beyer>{{cite journal | doi = 10.2307/4145019 | last1 = Beyer | first1 = W. A. | last2 = Zardecki | first2 = Andrew| issue = 1 | journal = [[American Mathematical Monthly]] | pages = 58–61 | title = The early history of the ham sandwich theorem | volume = 111 | year = 2004 | jstor = 4145019| url = https://zenodo.org/record/1235195 | id = {{ProQuest|203746537}} }}</ref>

<ref name=cluster>{{cite journal |last1=Lindsten |first1=Frederik |last2=Ohlsson |first2=Frederik |first3=Ljung |last3=Lennard |year=2011 |title=Just Relax and Come Clustering. A Convexification of k-means Clustering |journal=Technical Report from Automatic Control at Linköpings Universitet |page=1 |publisher=Linköping University }}</ref>

<ref name="jaslo">{{cite web |url=http://www.jaslo.pl/Miasto_Jaslo/Honorowi_Obywatele/Dyonizy_Steinhaus_Hugo |title=Steinhaus Hugo Dyonizy |author=Official webpage of the town of Jasło |year=2010 |work=Mieszkaniec: Steinhaus Hugo Dyonizy |publisher=Jasło. Moje miasto, nasz wspólny dom. |access-date=16 August 2011 |url-status=dead |archive-url=https://web.archive.org/web/20111001040917/http://www.jaslo.pl/Miasto_Jaslo/Honorowi_Obywatele/Dyonizy_Steinhaus_Hugo |archive-date=1 October 2011 }}</ref>

<ref name="kac">{{cite journal |last1=Kac |first1=Mark |year=1974 |title=Hugo Steinhaus--A Reminiscence and a Tribute |journal=[[The American Mathematical Monthly]] |volume=81 |issue=6 |pages=572–581 |publisher=Mathematical Association of America |doi=10.2307/2319205 |url=http://poncelet.math.nthu.edu.tw/disk5/js/biography/steinhaus.pdf |jstor=2319205 |archive-url=https://web.archive.org/web/20110927235225/http://poncelet.math.nthu.edu.tw/disk5/js/biography/steinhaus.pdf |archive-date=2011-09-27 |url-status=dead }}</ref>

<ref name="kac2">{{cite book |title=Enigmas of chance: an autobiography |last=Kac |first=Mark |author-link=Mark Kac |year=1987 |publisher=University of California Press |isbn= 978-0-520-05986-3|pages=49–53 |url=https://books.google.com/books?id=1ZWl39UJWycC&q=steinhaus+Grzegorz+Krochmalny&pg=PA50 }}</ref>

<ref name="mac">{{cite web |url=http://www-history.mcs.st-and.ac.uk/history/Biographies/Steinhaus.html |title=Hugo Dyonizy Steinhaus |author=John O'Connor |author2=Edmund F. Robertson |date=February 2000 |work=The MacTutor History of Mathematics archive |publisher=School of Mathematics and Statistics, University of St Andrews, Scotland |access-date=16 August 2011|author2-link=Edmund F. Robertson }}</ref>

<ref name=ortho>{{cite book|author1=Stefan Kaczmarz|author2=Hugo Steinhaus|title=Theorie der Orthogonalreihen|url=https://books.google.com/books?id=rGHQAAAAMAAJ|access-date=2 September 2011|year=1951|publisher=Chelsea Pub. Co.}}</ref>

<ref name=rok>{{cite web |url=http://www.im.pwr.wroc.pl/~hugo/HSC/imprezy/rok.html |title=2002-Rok Hugona Steinhausa (2002 - Year of Hugo Steinhaus) |author=Aleksander Weron |date=January 4, 2002 |publisher=[[Politechnika Wrocławska]] |access-date=26 August 2011}}</ref>

<ref name=slownikr>{{Citation|last=Steinhaus|first=Hugo|title=Słownik racjonalny|volume=I|year=1980|publisher=Zakład Narodowy im. Ossolińskich|language=pl|oclc=7272718}}</ref>

<ref name=wroc2>{{cite web|url=http://www.im.pwr.wroc.pl/~hugo/HSC/Steinhaus.htm|title=Prof. Hugo Steinhaus|publisher=Wrocław University of Technology}}</ref>

<ref name=sur>{{cite web|last=Steinhaus|url=http://matwbn.icm.edu.pl/ksiazki/cm/cm2/cm2145.pdf|title=Sur la liaison et la division des points d'un ensemble fini|publisher=Polish Virtual Library of Science - Mathematical Collection|year=1951|display-authors=etal}}</ref>

<ref name=uniw>{{cite web |url=http://www.uni.wroc.pl/o-nas/godno%C5%9Bci-honorowe/doktorzy-honoris-causa/hugo-steinhaus |title=Hugo Steinhaus |author=Monika Śliwa |date=May 4, 2010 |publisher=University of Wrocław |url-status=dead |archive-url=https://web.archive.org/web/20111005175329/http://www.uni.wroc.pl/o-nas/godno%C5%9Bci-honorowe/doktorzy-honoris-causa/hugo-steinhaus |archive-date=October 5, 2011 }}</ref>

<ref name="wprost">{{cite news |title=Wrocław Europy |author=Chełminiak, Wiesław |url=http://www.wprost.pl/ar/13078/Wroclaw-Europy/?O=13078&pg=2 |newspaper=Wprost |year=2002 |access-date=20 August 2011}}</ref>

<ref name="wroc">{{cite journal |last1=Duda |first1=Roman |year=2005 |title=Początki Matematyki w Powojennym Wrocławiu |journal=Przegląd Uniwesytetcki |issue=September |publisher=Polskie Towarzystwo Matematyczne. Oddział Wrocławski |url=http://www.math.uni.wroc.pl/ptm/Zjazd2005_PublikacjePrasowe/MatemPowoWroclawDuda.pdf |access-date=2011-08-17 |archive-date=2011-09-27 |archive-url=https://web.archive.org/web/20110927040243/http://www.math.uni.wroc.pl/ptm/Zjazd2005_PublikacjePrasowe/MatemPowoWroclawDuda.pdf |url-status=dead }}</ref>

<ref name="Orzel">{{Citation|last=Steinhaus|first=Hugo|title=Orzeł czy reszka |volume=I|year=1961| publisher=Państwowe Wydaw. Naukowe | publication-place=Warszawa |language=pl|oclc=68678009}}</ref>
}}

===Further reading===
* [[Kazimierz Kuratowski]], ''A Half Century of Polish Mathematics:  Remembrances and Reflections'', Oxford, [[Pergamon Press]], 1980, {{isbn|978-0-08-023046-7}}, pp.&nbsp;173–79 ''et passim''.
* Hugo Steinhaus, ''Mathematical Snapshots'', second edition, Oxford, 1951, [[blurb]].

==External links==
* {{MathGenealogy|id=7383}}
* [https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=227679 Hugo Steinhaus] in [[MathSciNet]] 
* [https://zbmath.org/authors/?q=ai%3Asteinhaus.hugo Hugo Steinhaus] in [[Zentralblatt MATH]]

{{Authority control}}

{{DEFAULTSORT:Steinhaus, Hugo}}
[[Category:1887 births]]
[[Category:1972 deaths]]
[[Category:Lwów School of Mathematics]]
[[Category:Jews from Galicia (Eastern Europe)]]
[[Category:Members of the Lwów Scientific Society]]
[[Category:Members of the Polish Academy of Learning]]
[[Category:Members of the Polish Academy of Sciences]]
[[Category:People from Jasło]]
[[Category:Jewish atheists]]
[[Category:Polish atheists]]
[[Category:Polish legionnaires (World War I)]]
[[Category:Probability theorists]]
[[Category:Game theorists]]
[[Category:University of Notre Dame faculty]]
[[Category:Recipients of the State Award Badge (Poland)]]
[[Category:Fair division researchers]]
[[Category:Recipients of the Medal of the 10th Anniversary of the People's Republic of Poland]]