MATHEMATICIANS GOING EAST a Lot Is Written About Emigration Of
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Ernst Zermelo Heinz-Dieter Ebbinghaus in Cooperation with Volker Peckhaus Ernst Zermelo
Ernst Zermelo Heinz-Dieter Ebbinghaus In Cooperation with Volker Peckhaus Ernst Zermelo An Approach to His Life and Work With 42 Illustrations 123 Heinz-Dieter Ebbinghaus Mathematisches Institut Abteilung für Mathematische Logik Universität Freiburg Eckerstraße 1 79104 Freiburg, Germany E-mail: [email protected] Volker Peckhaus Kulturwissenschaftliche Fakultät Fach Philosophie Universität Paderborn War burger St raße 100 33098 Paderborn, Germany E-mail: [email protected] Library of Congress Control Number: 2007921876 Mathematics Subject Classification (2000): 01A70, 03-03, 03E25, 03E30, 49-03, 76-03, 82-03, 91-03 ISBN 978-3-540-49551-2 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad- casting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant pro- tective laws and regulations and therefore free for general use. Typesetting by the author using a Springer TEX macro package Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 46/3100/YL - 5 4 3 2 1 0 To the memory of Gertrud Zermelo (1902–2003) Preface Ernst Zermelo is best-known for the explicit statement of the axiom of choice and his axiomatization of set theory. -
Albert Einstein
THE COLLECTED PAPERS OF Albert Einstein VOLUME 15 THE BERLIN YEARS: WRITINGS & CORRESPONDENCE JUNE 1925–MAY 1927 Diana Kormos Buchwald, József Illy, A. J. Kox, Dennis Lehmkuhl, Ze’ev Rosenkranz, and Jennifer Nollar James EDITORS Anthony Duncan, Marco Giovanelli, Michel Janssen, Daniel J. Kennefick, and Issachar Unna ASSOCIATE & CONTRIBUTING EDITORS Emily de Araújo, Rudy Hirschmann, Nurit Lifshitz, and Barbara Wolff ASSISTANT EDITORS Princeton University Press 2018 Copyright © 2018 by The Hebrew University of Jerusalem Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA (Revised for volume 15) Einstein, Albert, 1879–1955. The collected papers of Albert Einstein. German, English, and French. Includes bibliographies and indexes. Contents: v. 1. The early years, 1879–1902 / John Stachel, editor — v. 2. The Swiss years, writings, 1900–1909 — — v. 15. The Berlin years, writings and correspondence, June 1925–May 1927 / Diana Kormos Buchwald... [et al.], editors. QC16.E5A2 1987 530 86-43132 ISBN 0-691-08407-6 (v.1) ISBN 978-0-691-17881-3 (v. 15) This book has been composed in Times. The publisher would like to acknowledge the editors of this volume for providing the camera-ready copy from which this book was printed. Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources. Printed in the United States of America 13579108642 INTRODUCTION TO VOLUME 15 The present volume covers a thrilling two-year period in twentieth-century physics, for during this time matrix mechanics—developed by Werner Heisenberg, Max Born, and Pascual Jordan—and wave mechanics, developed by Erwin Schrödinger, supplanted the earlier quantum theory. -
Algebraic Generality Vs Arithmetic Generality in the Controversy Between C
Algebraic generality vs arithmetic generality in the controversy between C. Jordan and L. Kronecker (1874). Frédéric Brechenmacher (1). Introduction. Throughout the whole year of 1874, Camille Jordan and Leopold Kronecker were quarrelling over two theorems. On the one hand, Jordan had stated in his 1870 Traité des substitutions et des équations algébriques a canonical form theorem for substitutions of linear groups; on the other hand, Karl Weierstrass had introduced in 1868 the elementary divisors of non singular pairs of bilinear forms (P,Q) in stating a complete set of polynomial invariants computed from the determinant |P+sQ| as a key theorem of the theory of bilinear and quadratic forms. Although they would be considered equivalent as regard to modern mathematics (2), not only had these two theorems been stated independently and for different purposes, they had also been lying within the distinct frameworks of two theories until some connections came to light in 1872-1873, breeding the 1874 quarrel and hence revealing an opposition over two practices relating to distinctive cultural features. As we will be focusing in this paper on how the 1874 controversy about Jordan’s algebraic practice of canonical reduction and Kronecker’s arithmetic practice of invariant computation sheds some light on two conflicting perspectives on polynomial generality we shall appeal to former publications which have already been dealing with some of the cultural issues highlighted by this controversy such as tacit knowledge, local ways of thinking, internal philosophies and disciplinary ideals peculiar to individuals or communities [Brechenmacher 200?a] as well as the different perceptions expressed by the two opponents of a long term history involving authors such as Joseph-Louis Lagrange, Augustin Cauchy and Charles Hermite [Brechenmacher 200?b]. -
226 NAW 5/2 Nr. 3 September 2001 Honderdjaarslezing Dirk Struik Dirk Struik Honderdjaarslezing NAW 5/2 Nr
226 NAW 5/2 nr. 3 september 2001 Honderdjaarslezing Dirk Struik Dirk Struik Honderdjaarslezing NAW 5/2 nr. 3 september 2001 227 Afscheid van Dirk Struik Honderdjaarslezing Op 21 oktober 2000 overleed Dirk Struik in kringen. Zij ging een heel andere richting uit vriend Klaas Kooyman, de botanist die later zijn huis in Belmont (Massachusetts). Een In dan Anton en ik. Ik heb natuurlijk in die hon- bibliothecaris in Wageningen is geworden, La- Memoriam verscheen in het decembernum- derd jaar zoveel meegemaakt, dat ik in een tijn en Grieks geleerd bij meneer De Vries in mer van het Nieuw Archief. Ter afscheid van paar kwartier dat niet allemaal kan vertellen. Den Haag. We gingen daarvoor op en neer met deze beroemde wetenschapper van Neder- Ik zal een paar grepen doen uit mijn leven, het electrische spoortje van Rotterdam naar landse afkomst publiceren we in dit nummer mensen die me bijzonder hebben geboeid en Den Haag. We hebben er alleen maar het een- vijf artikelen over Dirk Struik. Het eerste ar- gebeurtenissen die me hebben be¨ınvloed. voudigste Latijn en Grieks geleerd, Herodo- tikel is van Struik zelf. In oktober 1994 orga- Mijn vroegste herinnering is aan de Boe- tus, Caesar — De Bello Gallico: “Gallia divisa niseerde het CWI een symposium ter ere van renoorlog, omstreeks 1900.2 Ik was een jaar est in partes tres ...” Dat heeft me heel wei- de honderdste verjaardag van Dirk Struik. Ter of vijf, zes en vroeg aan mijn vader: “Vader, nig geholpen bij de studie van de wiskunde. afsluiting heeft Struik toen zelf de volgen- wat betekent toch dat woord oorlog?” — dat Je kunt heel goed tensors doen zonder Latijn de redevoering gehouden, met als geheugen- hoef je tegenwoordig niet meer uit te leggen- te kennen, hoewel het wel goed is om te we- steun enkel wat aantekeningen op een velle- aan zesjarigen. -
How to Study Mathematics – the Manual for Warsaw University 1St Year Students in the Interwar Period
TECHNICAL TRANSACTIONS CZASOPISMO TECHNICZNE FUNDAMENTAL SCIENCES NAUKI PODSTAWOWE 2-NP/2015 KALINA BARTNICKA* HOW TO STUDY MATHEMATICS – THE MANUAL FOR WARSAW UNIVERSITY 1ST YEAR STUDENTS IN THE INTERWAR PERIOD JAK STUDIOWAĆ MATEMATYKĘ – PORADNIK DLA STUDENTÓW PIERWSZEGO ROKU Z OKRESU MIĘDZYWOJENNEGO Abstract In 1926 and in 1930, members of Mathematics and Physics Students’ Club of the Warsaw University published the guidance for the first year students. These texts would help the freshers in constraction of the plans and course of theirs studies in the situation of so called “free study”. Keywords: Warsaw University, Interwar period, “Free study”, Study of Mathematics, Freshers, Students’ clubs, Guidance for students Streszczenie W 1926 r. i w 1930 r. Koło Naukowe Matematyków i Fizyków Studentów Uniwersytetu War- szawskiego opublikowało poradnik dla studentów pierwszego roku matematyki. Są to teksty, które pomagały pierwszoroczniakom w racjonalnym skonstruowaniu planu i toku ich studiów w warunkach tzw. „wolnego stadium”. Słowa kluczowe: Uniwersytet Warszawski, okres międzywojenny, „wolne stadium”, studio wanie matematyki, pierwszoroczniacy, studenckie koła naukowe, poradnik dla studentów DOI: 10.4467/2353737XCT.15.203.4408 * L. & A. Birkenmajetr Institute of History of Science, Polish Academy of Sciences, Warsaw, Poland; [email protected] 14 This paper is focused primarily on the departure from the “free study” in university learning in Poland after it regained its independence in 1918. The idea of the “free study” had been strongly cherished by professors and staff of the Philosophy Department of Warsaw University even though the majority of students (including the students of mathematics and physics) were not interested in pursuing an academic career. The concept of free study left to the students the decision about the choice of subjects they wished to study and about the plan of their work. -
Obituary: FELIX POLLACZEK Felix Pollaczek Was Born on 1 December
Obituary: FELIX POLLACZEK Felix Pollaczek was born on 1 December 1892 in Vienna, Austria; he was the descendant of a well-known mid-European Jewish family which for several centuries had counted many learned men amongst its members. He became a Frenchman by naturalization in 1947. He obtained his scientific education and training at the Latin grammar school of Vienna, and at the Technical Univer- sities of Vienna and Brno (Czechoslovakia); he later studied mathematics at the University of Berlin. A master's degree in electrical engineering in 1920 from Brno was followed by a doctoral degree in mathematics in 1922 from Berlin with a thesis on number theory. This was concerned with the fields generated by the Ith and 12th roots of one, I being an irregular prime number. His first paper, on number theory, dates from 1917. He was employed in 1921 as an engineer by A.E.G. in Berlin. Then, in 1923, he became scientific adviser to the German Postal, Telephone and Telegraph Services at Reichspost-Zentralamt Berlin-Tempelhof. As a result of the political situation in Germany in 1933, he was dismissed from his post and then left the country. In Paris he made his living as a consulting engineer for the Societe d'Etudes pour Liaisons Telephoniques et Telegraphiques. In 1939-1940 and again from 1944 on, he held the position of Maitre de Recherches at the Centre National de la Recherche Scientifique in Paris. Felix Pollaczek's fruitful life came to an end on 29 April 1981 at Boulogne- Billancourt. In 1977 Pollaczek was awarded the John von Neumann Theory Prize by the ORSA-TIMS prize committee. -
Dirk Jan Struik (1894–2000)
mem-struik.qxp 5/30/01 10:32 AM Page 584 Dirk Jan Struik (1894–2000) Chandler Davis, Jim Tattersall, Joan Richards, and Tom Banchoff Dirk Struik giving a talk at his own 100th birthday celebration, September 1994, Brown University. (Photographs by John Forasté.) Dirk Jan Struik was born in Rotterdam on Kenneth O. May Prize for the History of Mathematics September 30, 1894. He attended the Hogere Burger from the International Commission on the History School from 1906 to 1911 and the University of of Mathematics. He died October 21, 2000, at his Leiden from 1912 to 1917. He spent the next seven home in Belmont, Massachusetts. years at the Technische Hogeschool in Delft as an —Jim Tattersall assistant mathematician to J. A. Schouten. In 1922, under the supervision of the geometer Willem van Chandler Davis der Woude, Struik received his Ph.D. in mathe- Dirk Jan Struik and his wife, Ruth Ramler Struik, matics from the University of Leiden. As the were the first research mathematicians I knew. In recipient of a Rockefeller Fellowship from 1924 to the 1930s, when I was in school, I knew them as 1926, he studied at the University of Rome and at friends of my parents. They encouraged me in the University of Göttingen. He began his career in mathematics and in social criticism. They remained the United States as a lecturer in mathematics at my friends up till Ruth’s death in 1993 and Dirk’s the Massachusetts Institute of Technology (MIT) in in 2000. Their eldest daughter, Rebekka Struik, the autumn of 1926. -
Adolf Lindenbaum: Notes on His Life, with Bibliography and Selected References
CORE Metadata, citation and similar papers at core.ac.uk Provided by Springer - Publisher Connector Log. Univers. 8 (2014), 285–320 c 2014 The Author(s). This article is published with open access at Springerlink.com 1661-8297/14/030285-36, published online December 3, 2014 DOI 10.1007/s11787-014-0108-2 Logica Universalis Adolf Lindenbaum: Notes on his Life, with Bibliography and Selected References Jan Zygmunt and Robert Purdy Abstract. Notes on the life of Adolf Lindenbaum, a complete bibliography of his published works, and selected references to his unpublished results. Mathematics Subject Classification. 01A60, 01A70, 01A73, 03-03. Keywords. Adolf Lindenbaum, biography, bibliography, unpublished works. This paper is dedicated to Adolf Lindenbaum (1904–1941)—Polish- Jewish mathematician and logician; a member of the Warsaw school of mathe- matics under Waclaw Sierpi´nski and Stefan Mazurkiewicz and school of math- ematical logic under JanLukasiewicz and Stanislaw Le´sniewski;1 and Alfred Tarski’s closest collaborator of the inter-war period. Our paper is divided into three main parts. The first part is biograph- ical and narrative in character. It gathers together what little is known of Lindenbaum’s short life. The second part is a bibliography of Lindenbaum’s published output, including his public lectures. Our aim there is to be complete and definitive. The third part is a list of selected references in the literature attesting to his unpublished results2 and delineating their extent. Just to confuse things, we name the second and third parts of our paper, respectively, “Bibliography Part One” and “Bibliography Part Two”. Why, we no longer remember. -
Multilinear Algebra and Chess Endgames
Games of No Chance MSRI Publications Volume 29, 1996 Multilinear Algebra and Chess Endgames LEWIS STILLER Abstract. This article has three chief aims: (1) To show the wide utility of multilinear algebraic formalism for high-performance computing. (2) To describe an application of this formalism in the analysis of chess endgames, and results obtained thereby that would have been impossible to compute using earlier techniques, including a win requiring a record 243 moves. (3) To contribute to the study of the history of chess endgames, by focusing on the work of Friedrich Amelung (in particular his apparently lost analysis of certain six-piece endgames) and that of Theodor Molien, one of the founders of modern group representation theory and the first person to have systematically numerically analyzed a pawnless endgame. 1. Introduction Parallel and vector architectures can achieve high peak bandwidth, but it can be difficult for the programmer to design algorithms that exploit this bandwidth efficiently. Application performance can depend heavily on unique architecture features that complicate the design of portable code [Szymanski et al. 1994; Stone 1993]. The work reported here is part of a project to explore the extent to which the techniques of multilinear algebra can be used to simplify the design of high- performance parallel and vector algorithms [Johnson et al. 1991]. The approach is this: Define a set of fixed, structured matrices that encode architectural primitives • of the machine, in the sense that left-multiplication of a vector by this matrix is efficient on the target architecture. Formulate the application problem as a matrix multiplication. -
Volume 9, Number 4 N~NSLETTER July-August 1979 PRESIDENT' S REPORT Duluth Meeting. the 1979 AWM Summer Meeting Will Be Held at T
Volume 9, Number 4 N~NSLETTER July-August 1979 **************************************************************************************** PRESIDENT' S REPORT Duluth meeting. The 1979 AWM summer meeting will be held at the joint mathematics meetings at the University of Minnesota in Duluth. All of our scheduled events will be on Thursday, August 23. They are: a panel discussion at 4 p.m. in Bohannon 90 on "Math education: a feminist per- spective." Moderator: Judy Roltman, University of Kansas Panelists: Lenore Blum, Mills College Deborah Hughes Hallett, Harvard University Diane Resek, San Francisco State University We also hope to have materials to present from a re-entry program in the De Anza Community College District (California). a business meeting at 5 p.m. in Bohannon 90 (following the panel). Agenda: new by-laws Goal: to get a members' consensus on new by-laws to be voted on in the fall by mail ballot. a wine and cheese party at 8 p.m. in the lounge of the Kirby Student Center. There will also be an AWM table staffed throughout the meeting. Volunteers are needed to staff it - check with us when you come to the meetings. Come on by and visitl bring your friends too. Also in Duluth: the MAA's HedrIck Lectures will be presented by Mary Ellen Rudin of the Universlty of Wisconsin, Madison. By-laws. The by-laws will be written up by mld-July, and available from the AWM office. Suggestions and amendments are welcome. The procedure is that they will be presented at Duluth for amendment and non-blnding sense-of-the-meeting comments. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
Alice in the Wonderful Land of Logical Notions)
The Mystery of the Fifth Logical Notion (Alice in the Wonderful Land of Logical Notions) Jean-Yves Beziau University of Brazil, Rio de Janeiro, Brazilian Research Council and Brazilian Academy of Philosophy [email protected] Abstract We discuss a theory presented in a posthumous paper by Alfred Tarski entitled “What are logical notions?”. Although the theory of these logical notions is something outside of the main stream of logic, not presented in logic textbooks, it is a very interesting theory and can easily be understood by anybody, especially studying the simplest case of the four basic logical notions. This is what we are doing here, as well as introducing a challenging fifth logical notion. We first recall the context and origin of what are here called Tarski- Lindenbaum logical notions. In the second part, we present these notions in the simple case of a binary relation. In the third part, we examine in which sense these are considered as logical notions contrasting them with an example of a non-logical relation. In the fourth part, we discuss the formulations of the four logical notions in natural language and in first- order logic without equality, emphasizing the fact that two of the four logical notions cannot be expressed in this formal language. In the fifth part, we discuss the relations between these notions using the theory of the square of opposition. In the sixth part, we introduce the notion of variety corresponding to all non-logical notions and we argue that it can be considered as a logical notion because it is invariant, always referring to the same class of structures.