Translated by Abe Shenitzer Edited by Robert G. Burns, Irena Szymaniec and Aleksander Weron

Vita 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 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. 2 (1945–1968) 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 Department of Mathematics and Statistics York University Toronto, Ontario, Canada Irena Szymaniec Wrocław, Poland Aleksander Weron The Hugo Steinhaus Center Wrocław University of Technology Wrocław, Poland Vita Mathematica ISBN 978-3-319-23101-3 ISBN 978-3-319-23102-0 (eBook) DOI 10.1007/978-3-319-23102-0 Library of Congress Control Number: 2015954183 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 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) 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. v vi 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 mathematical 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 vii 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

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