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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.

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