Vita Mathematica

Volume 18

Edited by Martin MattmullerR

More information about this series at http://www.springer.com/series/4834 Hugo Steinhaus

Mathematician for All Seasons Recollections and Notes, Vol. 1 (1887–1945)

Translated by Abe Shenitzer Edited by Robert G. Burns, Irena Szymaniec and Aleksander Weron Author Hugo Steinhaus (1887–1972)

Translator Abe Shenitzer Brookline, MA, USA

Editors Robert G. Burns York University Dept. Mathematics & Statistics Toronto, ON, Canada

Irena Szymaniec Wrocław, Poland

Aleksander Weron The Hugo Steinhaus Center Wrocław University of Technology Wrocław, Poland

Vita Mathematica ISBN 978-3-319-21983-7 ISBN 978-3-319-21984-4 (eBook) DOI 10.1007/978-3-319-21984-4

Library of Congress Control Number: 2015954183

Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Cover credit: Photo of Hugo Steinhaus. Courtesy of Hugo Steinhaus Center Archive, Wrocław University of Technology

Printed on acid-free paper

Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.birkhauser-science.com) Foreword to the First Polish Edition (1992)

You hold in your hands a record of the memories of Hugo Steinhaus, eminent mathematician, a founder of the Polish School of Mathematics, first-rate lecturer and writer, and one of the most formidable minds I have encountered. His steadfast gaze, wry sense of humor (winning him enemies as well as admirers), and penetrating critical and skeptical take on the world and the people in it, combined in an impression of brilliance when I, for the first time, conversed with him. I know that many others, including some of the most eminent of our day, also experienced a feeling of bedazzlement in his presence. In my first conversation with professor Steinhaus, he attempted to explain to me, someone who never went beyond high school mathematics, what that discipline is and what his own contribution to it was. He told me then—I took notes for later perusal—the following, more or less. It is often thought that mathematics is the science of numbers; this is in fact what Courant and Robbins claim in their celebrated book What is Mathematics?. However, this is not correct: higher mathematics does indeed include the study of number relations but a welter of non- numerical concepts besides. The essence of mathematics is the deepest abstraction, the purest logical thought, with the mind’s activity mediated by pen and paper. And there is no resorting to the senses of hearing, sight, or touch beyond this in the exercise of pure ratiocination. Moreover, of any given piece of mathematics it can never be assumed that it will turn out to be “useful”. Yet many mathematical discoveries have turned out to have amazingly effective applications—indeed, the modern world would be nothing like what it is without mathematics. For instance, there would be no rockets flying to other planets, no applications of atomic energy, no steel bridges, no Bureaux of Statistics, international communications, number-based games, radio, radar, precision bombardment, public opinion surveys, or regulation of processes of production. However, despite all this, mathematics is not at its heart an applied science: whole branches of mathematics continue to develop without there being any thought given to their applicability, or the likelihood of applications. Consider, for instance, “primes”, the whole numbers not factorable as products of two smaller whole numbers. It has long been known that there are infinitely many such numbers,

v vi Foreword to the First Polish Edition (1992) and among them there are “twins”, such as 3 and 5, 5 and 7, 11 and 13, 17 and 19, and so on. It is probable that there are infinitely many such twins, but no one has as yet managed to prove this, despite a great many attempts, all without the slightest potential practical application in view. The late Zygmunt Janiszewski, a brilliant mathematician, wrote: “I do mathe- matics in order to see how far one can get by means of pure reason.” The number of problems thought up by mathematicians but still waiting to be solved is unlimited. And among those for which solutions are found, only a few will find practical application. But it is mathematical abstraction that attracts the best minds—those capable of the purest kind of human mental activity, namely abstract thought. Hugo Steinhaus was of the opinion that the progress of mathematics is like a great march forward of humanity. But while the great mass of mankind has reached no further than the level of the cave-dweller, and a few have attained the level of the best of the middle ages, and even fewer the level of the eighteenth century, the question arises as to how many have reached the present level. He also said: “There is a continuing need to lead new generations along the thorny path which has no shortcuts. The Ancients said there is no royal road in mathematics. But the vanguard is leaving the great mass of pilgrims further and further behind, the procession is ever more strung out, and the leaders are finding themselves alone far out ahead.” *** However, Hugo Steinhaus’s recollections are to be read not so much in order to learn any mathematics—although one can glean from them interesting facts about what mathematicians have achieved. The main reasons for reading them are as follows: First, he led an interesting life, active and varied—although this is not to say that it was an easy one since the epithet “interesting” as used of life in our part of the world has often enough been a euphemism for experiences one would not wish on anyone. Second, his great sense of humor allows him to describe his experiences in unexpected ways. Third, his vast acquaintance—people fascinated him—included many interesting, important, and highly idiosyncratic individuals. And fourth and last, he always said what he thought, even though this sometimes brought trouble on him. Since he had no definite intention of publishing his writings, it follows that he was even franker in them. This truth-telling in response to difficult questions, this reluctance to smooth edges, not shrinking from assertions that may hurt some and induce in others uneasy feelings of moral discomfiture: this is perhaps the main virtue of these notes. The following were the chief character traits of the author of these notes: a sharp mind, a robust sense of humor, a goodly portion of shrewdness, and unusual acuteness of vision. For him, there was no spouting of slogans, popular myths, or propaganda, or resorting to comfortable beliefs. He frequently expressed himself bluntly, even violently, on many of the questions of his time—for instance, questions concerning interwar politics as it related to education (even though he, as a former Polish Legionnaire, might have been a beneficiary of them), general political problems, totalitarianism in its hitlerian and communist manifestations, and issues Foreword to the First Polish Edition (1992) vii of anti-Semitism and Polish-Jewish relations. He said many things people did not like back then, and things they don’t like today. I believe that especially today, when our reality is so different from that of Steinhaus’s time, it is well worthwhile to acquaint oneself with his spirit of contrariness and his sense of paradox, since these are ways of thinking that are today even more useful than in past times. ***

Steinhaus believed deeply in the potential for greatness and even perfection of the well-trained human mind. He often referred to the so-called “Ulam Principle” (named for the famous Polish mathematician Stanisław Ulam, who settled in the USA) according to which “the mathematician will do it better”, meaning that if two people are given a task to carry out with which neither of them is familiar, and one of them is a mathematician, then that one will do it better. For Steinhaus, this principle extended to practically every area of life and especially to those associated with questions related to economics. A particular oft-reiterated claim of his was that people who make decisions pertaining to large facets of public life—politics, the economy, etc.—should understand, in order to avoid mistakes and resultant damage, that there are things they don’t understand but which others do. But of course such understanding is difficult to attain and remains rare. Hugo Steinhaus represented what was best in that splendid flowering of the Polish intelligentsia of the first half of the twentieth century, without which our nation could never have survived to emerge reborn. This constituted a great impetus for good, triumphing over tanks, guns, and the secret police combined—a truly Polish strike force.

Kazimierz Dziewanowski1

1Kazimierz Dziewanowski (1930–1998), Polish writer, journalist, and diplomat. Polish ambas- sador to Washington 1990–1993.

Introduction to the English Edition

There are two well-known romantic anecdotes concerning Hugo Steinhaus. 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 “Lebesgue integral” spoken by one of two young men seated on a 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 1930s Steinhaus, Banach, and others used to frequent the “Scottish Café” in Lwów, where they would engage in animated mathematical discussions, using the marble tabletops to write on.1 At some point, Banach’s wife Łucja gave them a thick exercise book, and the “The Scottish Book”2 was born, in final form a collection of mathematical problems contributed by mathematicians since become legendary, with prizes for solutions noted, and including some solutions. It was destined to have a tremendous influence on world mathematics. 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 by Susan H. Case, published by Slapering Hol Press, 2002. From the review by Charles Martin: “This series of poems is loosely based upon the experiences of the mathematicians of The Scottish Café, who lived and worked in Lvov [Lwów], Poland, now [in] Ukraine. There is no theme more important for poetry to address in our time, when that life is imperiled by barbarisms from within and without. By recalling with celebratory joy the vigor, the messiness, the courage of that life as it was once lived in a terrible time by the patrons of The Scottish Café in Lvov, these poems do us a great service.” 2Available in English as: R. Daniel Mauldin (ed.), The Scottish Book, Birkhäuser Boston, Boston, MA, 1981. Steinhaus contributed ten problems to The Scottish Book, including the last, dated May 31, 1941, just days before the Nazis occupied Lwów.

ix x Introduction to the English Edition trigonometric series and his result concerning the problem of “fair division”, a forerunner of the “ham sandwich theorem”. These are just a few among the many notable contributions he made to a wide variety of areas of mathematics.3 He was the “father” of several outstanding mathematicians, including, in addition to Banach, the well-known mathematicians Kac, Orlicz, and Schauder, to name but three of those he supervised. He published extensively on both pure and applied topics. He was an inspired inventor. His popularization, entitled in English Mathematical Snapshots, is still in print. There is also an English translation of his One Hundred Problems in Elementary Mathematics published by Dover. 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 cosmopolitan culture of Lwów, where he was professor and dean between the wars. Being also of penetrating intelligence, unusual clarity of understanding, acerbic wit, given to outspokenness, and a Polish Jew, he was well equipped to pass comment on the period he lived through (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 cast of thousands. First, the halcyon pre-Great War days are chronicled: 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-Hungarian Empire, a first-class education at the regional Gymnasium, 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 description of 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 the interwar years—a period of Polish independence following well over a hundred years of foreign domination—which witnessed the above-mentioned blossoming of Polish mathematics of which he, at the University of Lwów, was a central figure, but also an intensifying nationalism and anti-Semitism. There then ensue the horrors of the two occupations. Just prior to the Soviet invasion we are given a chilling account of the chaotic situation at the Hungarian border whither many Poles—especially representatives of the Polish government— flee seeking refuge in Hungary. The indecision as to what the best course of action might be in appalling circumstances and the reigning sense of helplessness in the face of impending disaster are conveyed in vivid concrete terms without recourse

3See: Hugo Steinhaus, Selected Papers, PWN, Warsaw 1985. Introduction to the English Edition xi to emotional props. After assessing the situation insofar as that were possible, the Steinhauses decide to return to Lwów, where they are greeted by the sight of Red Army soldiers already in the streets. This first, Soviet, occupation, from September 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 makes for especially gripping, though harrowing, reading.) At the end of the war, following on the westward flight of the German army (and their spiteful razing of his beloved Jasło), the Steinhauses are able to emerge from their second hiding place. But then Poland is translated westwards by some hundreds of kilometers, so that Lwów becomes L0viv, a Ukrainian city, 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 and agricultural region of Poland. It is to this ruined city that Steinhaus eventually goes to assist in re-establishing the university and polytechnic. He helps to realize the goal of reconstituting in Wrocław what had been lost in Lwów by founding a mathematics school in Wrocław, this time of applied mathematics, and renewing the tradition of “The Scottish Book” with “The New Scottish Book”.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 ideology trumps basic common sense—a Poland subjugated to and exploited by the Soviet behemoth. (Thus we have here a sort of potted history of postwar Europe and America as viewed from inside Poland.) In the words of his former student Mark Kac, “[Hugo Steinhaus] 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.” 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 and natural dignity pursuing a life of integrity and demanding scientific and

4See: N. Davies and R. 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 separate institutions. xii Introduction to the English Edition intellectual enquiry in the face of encroaching calamity and chaos brought about chiefly by human ignorance and evil. In Wrocław, Steinhaus remains a well-known and very popular figure. In 1990, a Hugo Steinhaus Center was established, affiliated with the Wrocław Polytechnic. A “Café and Restaurant Steinhaus” was opened in 2012, and in 2013 his bust was put on display in the Wrocław Pantheon, located in the famous Wrocław City Hall. *** Publication History and Acknowledgments When Steinhaus’s diary ends in 1968, he is 81 years old, and the USSR seems to be a fixture of the world’s political scene. That is the year of the “Prague Spring” and widespread Polish student protests, and their brutal suppression, in the first case by Soviet tanks and in the second by police batons. Although some early portions of Steinhaus’s Recollections were published in the Polish magazine Znak 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 brought out by the London firm Aneks in 1992, while second and third editions were published by the publishing house “Atut” in 2002 and 2010, under the auspices of the Hugo Steinhaus Center. A German translation was published in 2010.6 The present English translation by Abe Shenitzer was edited first by Robert G. Burns, who also added footnotes considered necessary for an Anglophone reader, and chapter headings to facilitate cross-referencing among the footnotes. Since a great many inaccuracies had inevitably crept in, it was judged essential that a Polish expert edit the English text a second time, a task fulfilled to the letter by Irena Szymaniec, who also corrected and rationalized the footnotes. Aleksander Weron, the Director of the Hugo Steinhaus Center, oversaw the whole process, providing encouragement and final authority and expertise. We wish to thank all others who helped with the editorial process, in particular Edwin Beschler, Aleksander Garlicki, Ina Mette, Martin Muldoon, Patrick O’Keefe, Jim Tattersall, and Wojbor A. Woyczynski.´ 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, cartographer in the Geography Department of York University, for her superlative work making five of the maps. We wish the reader of these Recollections and Notes much pleasure from them.

Robert G. Burns Abe Shenitzer Irena Szymaniec Aleksander Weron

6Hugo Steinhaus, Erinnerungen und Aufzeichnungen, Neisse-Verlag, 2010. Introduction to the English Edition xiii

Editors’ Note on Polish Feminine Endings of Personal Names In the original work the Polish feminine endings -owa, indicating a woman’s married name, and -ówna, indicating her maiden name, are frequently used. These have been preserved in the present translation, including the index. Thus the index entry Steinhausówna (Kottowa), Lidia (Lidka), the author’s daughter refers to a female whose maiden name is Steinhaus, married name Kott, and first name Lidia, of which Lidka is an affectionate or diminutive version. The use of these endings was not uniform in the original, nor is it in the present translation. Thus, e.g., we have Mrs. Kossak instead of Kossakowa, and occasionally there occur hybrid forms where a married woman uses her maiden name.

Contents

Part I 1Jasło...... 3 2 The Gymnasium ...... 21 3 In the Capital Lwów...... 43 4 Göttingen ...... 51 5 The Return Home ...... 91 6 The Life of a Private Scholar ...... 105

Part II 7 IntheUniversityTownLwów...... 129 8 The First Occupation...... 229 Interlude: Flashes of Memory ...... 279 9 The Second Occupation ...... 287 10 Homeless Wandering ...... 295 11 Osiczyna ...... 315 Interlude: Flashes of Memory ...... 331 12 Stró˙ze ...... 335 13 Diary Entries ...... 385 AFlashofMemory...... 390

Index of Names ...... 467

xv