Table Of ContentVita Mathematica
19
Hugo Steinhaus
Mathematician
for All Seasons
Recollections and Notes,
Vol. 2 (1945–1968)
Translated by Abe Shenitzer
Edited by Robert G. Burns,
Irena Szymaniec and
Aleksander Weron
Vita Mathematica
Volume 19
Editedby
MartinMattmuRller
Moreinformationaboutthisseriesathttp://www.springer.com/series/4834
Hugo Steinhaus
Mathematician
for All Seasons
Recollections and Notes, Vol. 2 (1945–1968)
Translated by Abe Shenitzer
Edited by Robert G. Burns, Irena Szymaniec
and Aleksander Weron
Author
HugoSteinhaus(1887–1972)
Translator
AbeShenitzer
Brookline,MA,USA
Editors
RobertG.Burns
DepartmentofMathematicsandStatistics
YorkUniversity
Toronto,Ontario,Canada
IrenaSzymaniec
Wrocław,Poland
AleksanderWeron
TheHugoSteinhausCenter
WrocławUniversityofTechnology
Wrocław,Poland
VitaMathematica
ISBN978-3-319-23101-3 ISBN978-3-319-23102-0 (eBook)
DOI10.1007/978-3-319-23102-0
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Introduction to the English Edition
Therearetwowell-knownromanticanecdotesconcerningHugoSteinhaus.Follow-
ing a period of military service in the early part of World War I, he was given a
desk job in Kraków. In the summer of 1916, he went on a “random walk” from
his Kraków residence at 9 Karmelicka Street to Planty Park, where he overheard
the words“Lebesgueintegral”spokenbyone of two youngmenseated ona park
bench—none other than the self-taught lovers of mathematics Stefan Banach and
Otto Nikodým. Later Steinhaus would create, with Banach, the famous Lwów
school of mathematics, one of the two prominent Polish mathematics schools—
the other was in Warsaw—flourishing in Poland between the wars. According to
the second anecdote, in the 1930sSteinhaus, Banach, and others used to frequent
the“ScottishCafé” inLwów,wheretheywouldengageinanimatedmathematical
discussions,usingthemarbletabletopstowriteon.1 Atsomepoint,Banach’swife
Łucjagavethemathickexercisebook,andthe“TheScottishBook”2 wasborn,in
final form a collection of mathematical problems contributed by mathematicians
since become legendary, with prizes for solutions noted, and including some
solutions.Itwasdestinedtohaveatremendousinfluenceonworldmathematics.
In addition to “discovering” Banach and collaborating with him, Steinhaus
pioneered the foundations of probability theory, anticipating Kolmogorov, and of
game theory, anticipating von Neumann. He is also well known for his work on
1The mathematical activity connected with “The Scottish Café” has inspired a cycle of poems
bySusanH.Case,publishedbySlaperingHolPress,2002.FromthereviewbyCharlesMartin:
“ThisseriesofpoemsislooselybasedupontheexperiencesofthemathematiciansofTheScottish
Café,wholivedandworkedinLvov[Lwów],Poland,now[in]Ukraine.Thereisnothememore
importantforpoetrytoaddressinourtime,whenthatlifeisimperiledbybarbarismsfromwithin
andwithout.Byrecallingwithcelebratoryjoythevigor,themessiness,thecourageofthatlifeas
itwasoncelivedinaterribletimebythepatronsofTheScottishCaféinLvov,thesepoemsdous
agreatservice.”
2AvailableinEnglishas:R.DanielMauldin(ed.),TheScottishBook,BirkhäuserBoston,Boston,
MA,1981.SteinhauscontributedtenproblemstoTheScottishBook,includingthelast,datedMay
31,1941,justdaysbeforetheNazisoccupiedLwów.
v
vi IntroductiontotheEnglishEdition
trigonometric series and his result concerning the problem of “fair division”, a
forerunnerofthe “hamsandwichtheorem”.These are justa few amongthemany
notablecontributionshemadetoawidevarietyofareasofmathematics.3Hewasthe
“father”ofseveraloutstandingmathematicians,including,inadditiontoBanach,the
well-knownmathematiciansKac,Orlicz,andSchauder,tonamebutthreeofthose
hesupervised.Hepublishedextensivelyonbothpureandappliedtopics.Hewasan
inspiredinventor.His popularization,entitled in EnglishMathematicalSnapshots,
isstillinprint.ThereisalsoanEnglishtranslationofhisOneHundredProblemsin
ElementaryMathematicspublishedbyDover.
However, although his reminiscences and diary entries contain much of direct
mathematical interest or interest for the history of mathematics, and the mathe-
matical theme recurs throughout, they are of much wider interest. Steinhaus was
a man of high culture: he was well versed in science, read widely in philosophy
and literature, knew Latin, German, French, and English, was a great stickler for
linguistic accuracy—a disciple of Karl Kraus in this—and reveled in the vital
cosmopolitancultureofLwów,wherehewasprofessoranddeanbetweenthewars.
Beingalsoofpenetratingintelligence,unusualclarityofunderstanding,acerbicwit,
givento outspokenness,and a Polish Jew, he was well equippedto pass comment
ontheperiodhelivedthrough(1887–1972).
Thus, we have here a historical document of unusual general appeal reporting
on “interesting times” in an “interesting” part of the world—the inside story,
recounted unemotionally, with flair and sometimes scathing humor, and featuring
a castof thousands.First, the halcyonpre-GreatWar daysarechronicled:a rather
idyllic, if not privileged, childhood centered on his hometown Jasło in the region
of southern Poland known as Galicia, then part of the Austro-HungarianEmpire,
a first-class education at the regionalGymnasium, and a brief period as a student
at the University of Lwów before going off to Göttingen to do his Ph.D. under
Hilbert. (Here, in addition to a fascinating descriptionof that university town and
its student culture, we get interesting sketches of many of the mathematical and
scientific luminaries of those days.) Next we have a description of his role in the
early part of World War I as a member of a gun-crew, trundling their artillery
piece about the eastern theater of the war. This is followed by an elaboration of
theinterwaryears—aperiodofPolishindependencefollowingwelloverahundred
yearsofforeigndomination—whichwitnessedtheabove-mentionedblossomingof
Polishmathematicsofwhichhe,attheUniversityofLwów,wasacentralfigure,but
alsoanintensifyingnationalismandanti-Semitism.
There then ensue the horrors of the two occupations. Just prior to the Soviet
invasion we are given a chilling accountof the chaotic situation at the Hungarian
borderwhithermanyPoles—especiallyrepresentativesofthePolishgovernment—
fleeseekingrefugeinHungary.Theindecisionastowhatthebestcourseofaction
might be in appalling circumstancesand the reigning sense of helplessness in the
face of impending disaster are conveyedin vivid concrete terms without recourse
3See:HugoSteinhaus,SelectedPapers,PWN,Warsaw1985.
IntroductiontotheEnglishEdition vii
to emotionalprops. After assessing the situation insofar as thatwere possible, the
Steinhausesdecide to returnto Lwów, wherethey are greeted by the sight of Red
Armysoldiersalreadyinthestreets.Thisfirst,Soviet,occupation,fromSeptember
1939 to June 1941, is characterized by summary arrests and mass deportations,
hallmarks of Stalinist repression, hidden behind a thin veneer of normalcy. The
second occupation, this time by the Nazis, lasting from June 1941 to early 1945,
is marked by a more blatant, racially motivated brutality. Following a terrifying
period of evading arrest by moving from one friend’s residence to another, the
Steinhauses manage to find a provisional hiding-place in the countryside. (This
makesforespeciallygripping,thoughharrowing,reading.)
At the end of the war, following on the westward flight of the German army
(andtheir spitefulrazingof hisbelovedJasło), theSteinhausesare ableto emerge
from their second hiding place. But then Poland is translated westwards by some
hundredsof kilometers,so that Lwów becomesL0viv,a Ukrainiancity,and in the
west, Breslau on the Oder (completely destroyed by the war), formerly German,
becomes Wrocław,4 capital of Lower Silesia, later to become a great industrial
andagriculturalregionofPoland.ItistothisruinedcitythatSteinhauseventually
goestoassist inre-establishingtheuniversityandpolytechnic.He helpstorealize
the goal of reconstitutingin Wrocław what had been lost in Lwów by foundinga
mathematicsschoolinWrocław,thistimeofappliedmathematics,andrenewingthe
traditionof“TheScottishBook”with“TheNewScottishBook”.5
There now follows, in the form of diary entries, a long semi-tirade, laced with
irony and interspersed with assessments of local and international developments,
concerning the frustrations of living in a communist vassal state where distorted
ideologytrumpsbasiccommonsense—aPolandsubjugatedtoandexploitedbythe
Sovietbehemoth.(ThuswehavehereasortofpottedhistoryofpostwarEuropeand
AmericaasviewedfrominsidePoland.)
In the words of his former student Mark Kac, “[Hugo Steinhaus] was one of
thearchitectsoftheschoolofmathematicswhichfloweredmiraculouslyinPoland
betweenthetwo warsand itwashe who,perhapsmorethananyotherindividual,
helpedtoraisePolishmathematicsfromtheashestowhichithadbeenreducedby
the Second World War to the position of new strength and respect which it now
occupies.Hewasamanofgreatcultureandinthebestsenseofthewordaproduct
ofWesternCivilization.”
The overall impression of Steinhaus’s Recollections and Notes is of the com-
pelling record of a man of intelligence and steadfast intellectual honesty, good
sense andnaturaldignitypursuinga life ofintegrityanddemandingscientific and
4See: N. Davies andR. Moorhouse, Microcosm. Portrait of a Central European City, Jonathan
Cape,2002.
5In fact, he was the chief organizer and first dean of the Faculty of Mathematics, Physics, and
Chemistry, when, at this initial stage, the university and polytechnic in Wrocław were not yet
separateinstitutions.
viii IntroductiontotheEnglishEdition
intellectual enquiry in the face of encroaching calamity and chaos brought about
chieflybyhumanignoranceandevil.
InWrocław,Steinhausremainsawell-knownandverypopularfigure.In1990,a
HugoSteinhausCenterwasestablished,affiliatedwiththeWrocławPolytechnic.A
“CaféandRestaurantSteinhaus”wasopenedin2012,andin2013hisbustwasput
ondisplayintheWrocławPantheon,locatedinthefamousWrocławCityHall.
* * *
PublicationHistoryandAcknowledgments
When Steinhaus’sdiary ends in 1968, he is 81 years old, and the USSR seems to
be a fixtureof the world’spoliticalscene. Thatis the year of the “PragueSpring”
andwidespreadPolishstudentprotests,andtheirbrutalsuppression,inthefirstcase
bySoviettanksandin thesecondbypolicebatons.Althoughsomeearlyportions
ofSteinhaus’sRecollectionswere publishedinthe PolishmagazineZnak in 1970,
full publication was at that time out of the question for reasons which a perusal
of the later pages of the diary makes clear. The first complete Polish edition was
broughtoutbytheLondonfirmAneksin1992,whilesecondandthirdeditionswere
publishedbythepublishinghouse“Atut”in 2002and2010,undertheauspicesof
theHugoSteinhausCenter.AGermantranslationwaspublishedin2010.6
The presentEnglish translationbyAbe Shenitzerwas editedfirst byRobertG.
Burns, who also added footnotesconsiderednecessary for an Anglophonereader,
and chapter headings to facilitate cross-referencing among the footnotes. Since a
greatmanyinaccuracieshadinevitablycreptin,itwasjudgedessentialthataPolish
expert edit the English text a second time, a task fulfilled to the letter by Irena
Szymaniec,whoalso correctedandrationalizedthe footnotes.AleksanderWeron,
the Director of the Hugo Steinhaus Center, oversaw the whole process, providing
encouragementandfinalauthorityandexpertise.
We wishto thankallotherswhohelpedwiththeeditorialprocess,inparticular
EdwinBeschler,AleksanderGarlicki,InaMette,MartinMuldoon,PatrickO’Keefe,
Jim Tattersall, and Wojbor A. Woyczyn´ski. Special thanks are due to Martin
Mattmüller for many corrections and improvements, to Dorothy Mazlum for her
great rapport in connection with the production process, and to Carolyn King,
cartographerin the GeographyDepartmentof York University,for her superlative
workmakingfiveofthemaps.
WewishthereaderoftheseRecollectionsandNotesmuchpleasurefromthem.
RobertG.Burns
AbeShenitzer
IrenaSzymaniec
AleksanderWeron
6HugoSteinhaus,ErinnerungenundAufzeichnungen,Neisse-Verlag,2010.
IntroductiontotheEnglishEdition ix
Editors’NoteonPolishFeminineEndingsofPersonalNames
IntheoriginalworkthePolishfeminineendings-owa,indicatingawoman’smarried
name, and -ówna, indicating her maiden name, are frequently used. These have
beenpreservedinthepresenttranslation,includingtheindex.Thustheindexentry
Steinhausówna(Kottowa), Lidia (Lidka), the author’sdaughter refersto a female
whosemaidennameisSteinhaus,marriednameKott,andfirstnameLidia,ofwhich
Lidka is an affectionate or diminutive version. The use of these endings was not
uniformintheoriginal,norisitinthepresenttranslation.Thus,e.g.,wehaveMrs.
Kossak instead of Kossakowa, andoccasionallythere occur hybridformswhere a
marriedwomanuseshermaidenname.
