Refugee Mathematicians: a German Crisis and a British Response, 1933-L 936
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LINEAR ALGEBRA METHODS in COMBINATORICS László Babai
LINEAR ALGEBRA METHODS IN COMBINATORICS L´aszl´oBabai and P´eterFrankl Version 2.1∗ March 2020 ||||| ∗ Slight update of Version 2, 1992. ||||||||||||||||||||||| 1 c L´aszl´oBabai and P´eterFrankl. 1988, 1992, 2020. Preface Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent decades. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint at the plausibility of some link between the two areas. A more profound connection, the use of determinants in combinatorial enumeration goes back at least to the work of Kirchhoff in the middle of the 19th century on counting spanning trees in an electrical network. It is much less known, however, that quite apart from the theory of determinants, the elements of the theory of linear spaces has found striking applications to the theory of families of finite sets. With a mere knowledge of the concept of linear independence, unexpected connections can be made between algebra and combinatorics, thus greatly enhancing the impact of each subject on the student's perception of beauty and sense of coherence in mathematics. If these adjectives seem inflated, the reader is kindly invited to open the first chapter of the book, read the first page to the point where the first result is stated (\No more than 32 clubs can be formed in Oddtown"), and try to prove it before reading on. (The effect would, of course, be magnified if the title of this volume did not give away where to look for clues.) What we have said so far may suggest that the best place to present this material is a mathematics enhancement program for motivated high school students. -
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. -
Rudi Mathematici
Rudi Mathematici Y2K Rudi Mathematici Gennaio 2000 52 1 S (1803) Guglielmo LIBRI Carucci dalla Somaja Olimpiadi Matematiche (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE P1 (1912) Boris GNEDENKO 2 D (1822) Rudolf Julius Emmanuel CLAUSIUS Due matematici "A" e "B" si sono inventati una (1905) Lev Genrichovich SHNIRELMAN versione particolarmente complessa del "testa o (1938) Anatoly SAMOILENKO croce": viene scritta alla lavagna una matrice 1 3 L (1917) Yuri Alexeievich MITROPOLSHY quadrata con elementi interi casuali; il gioco (1643) Isaac NEWTON consiste poi nel calcolare il determinante: 4 M (1838) Marie Ennemond Camille JORDAN 5 M Se il determinante e` pari, vince "A". (1871) Federigo ENRIQUES (1871) Gino FANO Se il determinante e` dispari, vince "B". (1807) Jozeph Mitza PETZVAL 6 G (1841) Rudolf STURM La probabilita` che un numero sia pari e` 0.5, (1871) Felix Edouard Justin Emile BOREL 7 V ma... Quali sono le probabilita` di vittoria di "A"? (1907) Raymond Edward Alan Christopher PALEY (1888) Richard COURANT P2 8 S (1924) Paul Moritz COHN (1942) Stephen William HAWKING Dimostrare che qualsiasi numero primo (con (1864) Vladimir Adreievich STELKOV l'eccezione di 2 e 5) ha un'infinita` di multipli 9 D nella forma 11....1 2 10 L (1875) Issai SCHUR (1905) Ruth MOUFANG "Die Energie der Welt ist konstant. Die Entroopie 11 M (1545) Guidobaldo DEL MONTE der Welt strebt einem Maximum zu" (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR Rudolph CLAUSIUS 12 M (1906) Kurt August HIRSCH " I know not what I appear to the world, -
Math 126 Lecture 4. Basic Facts in Representation Theory
Math 126 Lecture 4. Basic facts in representation theory. Notice. Definition of a representation of a group. The theory of group representations is the creation of Frobenius: Georg Frobenius lived from 1849 to 1917 Frobenius combined results from the theory of algebraic equations, geometry, and number theory, which led him to the study of abstract groups, the representation theory of groups and the character theory of groups. Find out more at: http://www-history.mcs.st-andrews.ac.uk/history/ Mathematicians/Frobenius.html Matrix form of a representation. Equivalence of two representations. Invariant subspaces. Irreducible representations. One dimensional representations. Representations of cyclic groups. Direct sums. Tensor product. Unitary representations. Averaging over the group. Maschke’s theorem. Heinrich Maschke 1853 - 1908 Schur’s lemma. Issai Schur Biography of Schur. Issai Schur Born: 10 Jan 1875 in Mogilyov, Mogilyov province, Russian Empire (now Belarus) Died: 10 Jan 1941 in Tel Aviv, Palestine (now Israel) Although Issai Schur was born in Mogilyov on the Dnieper, he spoke German without a trace of an accent, and nobody even guessed that it was not his first language. He went to Latvia at the age of 13 and there he attended the Gymnasium in Libau, now called Liepaja. In 1894 Schur entered the University of Berlin to read mathematics and physics. Frobenius was one of his teachers and he was to greatly influence Schur and later to direct his doctoral studies. Frobenius and Burnside had been the two main founders of the theory of representations of groups as groups of matrices. This theory proved a very powerful tool in the study of groups and Schur was to learn the foundations of this subject from Frobenius. -
Mathematisches Forschungsinstitut Oberwolfach Emigration Of
Mathematisches Forschungsinstitut Oberwolfach Report No. 51/2011 DOI: 10.4171/OWR/2011/51 Emigration of Mathematicians and Transmission of Mathematics: Historical Lessons and Consequences of the Third Reich Organised by June Barrow-Green, Milton-Keynes Della Fenster, Richmond Joachim Schwermer, Wien Reinhard Siegmund-Schultze, Kristiansand October 30th – November 5th, 2011 Abstract. This conference provided a focused venue to explore the intellec- tual migration of mathematicians and mathematics spurred by the Nazis and still influential today. The week of talks and discussions (both formal and informal) created a rich opportunity for the cross-fertilization of ideas among almost 50 mathematicians, historians of mathematics, general historians, and curators. Mathematics Subject Classification (2000): 01A60. Introduction by the Organisers The talks at this conference tended to fall into the two categories of lists of sources and historical arguments built from collections of sources. This combi- nation yielded an unexpected richness as new archival materials and new angles of investigation of those archival materials came together to forge a deeper un- derstanding of the migration of mathematicians and mathematics during the Nazi era. The idea of measurement, for example, emerged as a critical idea of the confer- ence. The conference called attention to and, in fact, relied on, the seemingly stan- dard approach to measuring emigration and immigration by counting emigrants and/or immigrants and their host or departing countries. Looking further than this numerical approach, however, the conference participants learned the value of measuring emigration/immigration via other less obvious forms of measurement. 2892 Oberwolfach Report 51/2011 Forms completed by individuals on religious beliefs and other personal attributes provided an interesting cartography of Italian society in the 1930s and early 1940s. -
Historical Notes on Loop Theory
Comment.Math.Univ.Carolin. 41,2 (2000)359–370 359 Historical notes on loop theory Hala Orlik Pflugfelder Abstract. This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s. Keywords: quasigroup theory, loop theory, history Classification: Primary 01A60; Secondary 20N05 This paper is an attempt to map, to fit together not only in a geographical and a chronological sense but also conceptually, the various areas where loop theory originated and through which it moved during the early part of its 70 years of history. 70 years is not very much compared to, say, over 300 years of differential calculus. But it is precisely because loop theory is a relatively young subject that it is often misinterpreted. Therefore, it is extremely important for us to acknowledge its distinctive origins. To give an example, when somebody asks, “What is a loop?”, the simplest way to explain is to say, “it is a group without associativity”. This is true, but it is not the whole truth. It is essential to emphasize that loop theory is not just a generalization of group theory but a discipline of its own, originating from and still moving within four basic research areas — algebra, geometry, topology, and combinatorics. Looking back on the first 50 years of loop history, one can see that every decade initiated a new and important phase in its development. These distinct periods can be summarized as follows: I. 1920s the first glimmerings of non-associativity II. 1930s the defining period (Germany) III. 1940s-60s building the basic algebraic frame and new approaches to projective geometry (United States) IV. -
Canadian Society for History and Philosophy of Mathematics
BULLETIN CSHPMlSCHPM November/novembre 2000 Number/Ie numero 27 WHAT'S INSIDE President's Message [G. Van Brummelen] ........................................................................................ page 4 Articles The GodeI-Zermelo Letters [G. Moore] ............................................................................................. page 6 History of mathematics it Ia fran~aise [T. Archibald] ........................................................................ page 10 The Moscow Mathematical Society [Po Buckingham] ...................................................................... page 12 Web Review: www.maths.tcd.ie/publHistMath [R.Bradley] ............................................................ page 15 The Princeton Mathematics Community [R. Jantzen]. ...................................................................... page 16 Reports AMS Western Section ....................................................................................................................... page 2 Executive Council Minutes ................................................................................................................. page 3 Call for Papers: AMS Spring Sectional Meeting................................................................................ page 5 Minutes of the Annual General Meeting .................................................................................... page 9 Canadian Society for History and Philosophy of Mathematics Societe canadienne d'histoire et de philosophie des mathematiques -
Episodes in the History of Modern Algebra (1800–1950)
HISTORY OF MATHEMATICS • VOLUME 32 Episodes in the History of Modern Algebra (1800–1950) Jeremy J. Gray Karen Hunger Parshall Editors American Mathematical Society • London Mathematical Society Episodes in the History of Modern Algebra (1800–1950) https://doi.org/10.1090/hmath/032 HISTORY OF MATHEMATICS v VOLUME 32 Episodes in the History of Modern Algebra (1800–1950) Jeremy J. Gray Karen Hunger Parshall Editors Editorial Board American Mathematical Society London Mathematical Society Joseph W. Dauben Alex D. D. Craik Peter Duren Jeremy J. Gray Karen Parshall, Chair Robin Wilson, Chair MichaelI.Rosen 2000 Mathematics Subject Classification. Primary 01A55, 01A60, 01A70, 01A72, 01A73, 01A74, 01A80. For additional information and updates on this book, visit www.ams.org/bookpages/hmath-32 Library of Congress Cataloging-in-Publication Data Episodes in the history of modern algebra (1800–1950) / Jeremy J. Gray and Karen Hunger Parshall, editors. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-8218-4343-7 (alk. paper) ISBN-10: 0-8218-4343-5 (alk. paper) 1. Algebra—History. I. Gray, Jeremy, 1947– II. Parshall, Karen Hunger, 1955– QA151.E65 2007 512.009—dc22 2007060683 AMS softcover ISBN: 978-0-8218-6904-8 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. -
Professor ADDRESS: Department of Mathematics University of Florida
CURRICULUM VITAE NAME: Krishnaswami Alladi PRESENT POSITION: Professor ADDRESS: Department of Mathematics University of Florida Gainesville, Florida 32611 Ph: (352) 294-2290 e-mail: alladik@ufl.edu BORN: October 5, 1955 Trivandrum, India DEGREES: Ph.D., U.C.L.A. - 1978; Advisor-E.G. Straus M.A., U.C.L.A. - 1976 B.Sc., Madras University, India - 1975 RESEARCH INTERESTS: Number Theory - Analytic Number Theory, Sieve Methods, Probabilistic Number Theory, Diophantine Approximations, Partitions, q-hypergeometric identities PROFESSIONAL EXPERIENCE: T.H. Hildebrandt Research Assistant Professor, University of Michigan, Ann Arbor, Michigan, 1978-1981. Visiting Member, Institute for Advanced Study, Princeton, New Jersey, 1981-1982. Visiting Associate Professor, University of Texas, Austin, Texas, 1982-1983. Visiting Associate Professor, University of Hawaii, Honolulu, Hawaii, 1984-1985. Associate Professor, Institute of Mathematical Sciences, Madras, India, 1981-1986. Associate Professor, University of Florida, 1986-1989. Professor, University of Florida, 1989-present. Visiting Professor, Pennsylvania State University, University Park, Pennsylvania, in 1992-93 (on sabbatical from University of Florida) and in Fall 1994. Chairman, Department of Mathematics, University of Florida, 1998-2008 AWARDS AND HONORS: Chancellor's Fellowship for the Ph.D., 1975-78, UCLA. Alumni Medal for one of 5 best Ph.D. theses (all subjects) at UCLA in 1978. CLAS Research Awards at University of Florida thrice: 1987, 1994, 2000 TIP Award for distinguished teaching at the University of Florida in 1994-95. STEP/SPP Awards for distinguished performance in the rank of Full Professor at the University of Florida twice: 2001, 2010. Elected Fellow of the American Mathematical Society in 2012-13 during inaugural year of the Fellows Program of the AMS. -
Friedrich Karl Schmidt – Wikipedia
Friedrich Karl Schmidt – Wikipedia https://de.wikipedia.org/wiki/Friedrich_Karl_Schmidt Friedrich Karl Schmidt (* 22. September 1901 in Düsseldorf; † 25. Januar 1977 in Heidelberg) war ein deutscher Mathematiker, der sich vor allem mit Algebra und Zahlentheorie beschäftigte. Leben und Werk Literatur Weblinks Einzelnachweise Schmidt studierte 1920 bis 1925 in Freiburg und Marburg. 1925 promovierte er an der Albert-Ludwigs- Universität Freiburg bei Alfred Loewy über Allgemeine Körper im Gebiet der höheren Kongruenzen. 1927 Friedrich Karl Schmidt war er Privatdozent an der Universität Erlangen, wo er sich auch habilitierte und 1933 außerplanmäßiger Professor wurde. 1933/34 war er Dozent an der Universität Göttingen, wo er mit Helmut Hasse zusammenarbeitete, und danach bis 1946 Professor an der Universität Jena. Während der Kriegsjahre war er an der Deutschen Versuchsanstalt für Segelflug in Reichenhall. Nach dem Krieg wurde er 1946 Professor an der Westfälischen Wilhelms-Universität in Münster und von 1952 bis zu seiner Emeritierung 1966 an der Universität Heidelberg. Mitte der 1930er Jahre war er Mitherausgeber der Grundlehren der mathematischen Wissenschaften. Schmidt war seit 1954 Mitglied der Heidelberger Akademie der Wissenschaften[1] und wurde 1968 Ehrendoktor der FU Berlin. 1 von 3 21.02.2020, 08:18 Friedrich Karl Schmidt – Wikipedia https://de.wikipedia.org/wiki/Friedrich_Karl_Schmidt Schmidt ist vor allem für seine Beiträge zur Theorie der algebraischen Funktionenkörper und insbesondere für seine Definition einer Zetafunktion für Funktionenkörper und den Beweis des Riemann-Roch Satzes für Funktionenkörper (nicht nur über den komplexen Zahlen, sondern auch über anderen Körpern) bekannt. Daneben arbeitete er unter anderem zur Klassenkörpertheorie und zur Bewertungstheorie. Zu seinen Doktoranden zählen unter anderem Reinhardt Kiehl, Ernst Kunz, Hans-Joachim Nastold und Chiungtze Tsen. -
Emigration of Mathematicians from Outside German-Speaking Academia 1933–1963, Supported by the Society for the Protection of Science and Learning
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 39 (2012) 84–104 www.elsevier.com/locate/yhmat Emigration of mathematicians from outside German-speaking academia 1933–1963, supported by the Society for the Protection of Science and Learning Rolf Nossum * Department of Mathematics, University of Agder, P.O. Box 422, N-4604 Kristiansand, Norway Available online 14 September 2011 Abstract Racial and political persecution of German-speaking scholars from 1933 onward has already been exten- sively studied. The archives of the Society for the Protection of Science and Learning (SPSL), which are depos- ited in the Western Manuscripts Collection at the Bodleian Library in Oxford, is a rich source of information about the emigration of European scientists, also those who did not come from German-speaking institutions. This is an account of the support given by the SPSL to the persecuted mathematicians among them. The chal- lenges faced by these emigrants included, in addition to anti-Semitism and xenophobia in their countries both of origin and of destination, the restricted financial means of the SPSL, and the sometimes arbitrary assessment of academic merits. Ó 2011 Elsevier Inc. All rights reserved. Zusammenfassung Der rassistischen und politischen Verfolgung deutschsprachiger Wissenschaftler nach 1933 wurden bereits umfassende Studien gewidmet. Die Akten der Society for the Protection of Science and Learning (SPSL), die bei der Western Manuscripts Collection der Bodleian Library in Oxford deponiert sind, bieten umfangreiche Informationen zur Emigration auch derjenigen europäischen Wissenschaftler, die nicht deutschsprachig sozial- isiert waren. Hier soll die Unterstützung der SPSL für verfolgte nicht-deutschsprachige Mathematiker beschrie- ben werden. -
Walter Ledermann Walter Ledermann Passed Away Peacefully on 22 May 2009 in London Less Than Two Years Short of His 100Th Birthday
Walter Ledermann Walter Ledermann passed away peacefully on 22 May 2009 in London less than two years short of his 100th birthday. He was born into a Jewish family in Berlin on 18 March 1911, the second of four children. His father, William Ledermann, was a medical doctor and his mother, Charlotte née Apt, was the daughter of a wealthy metal merchant. He entered the Köllnisches Gymnasium in Berlin in 1917, progressing to the Leibniz Gymnasium in the same city in 1920. There he learnt classics, studying Latin for nine years and Greek for six years. The school also taught French but, as was usual at this time, not much science. Although very little mathematics was taught in German schools in general at this time, Walter had the advantage that the Leibniz Gymnasium taught more mathematics than other schools as a mark of respect for Gottfried von Leibniz after whom the school was named. He enjoyed studying the classics, especially Greek with its wonderful literature, but became fascinated by mathematics from his first lesson at the age of eleven. From that time on he decided to make mathematics his career. Also from age 11 he began learning to play the violin, the cost of a lesson in these times of hyperinflation being set at the cost of a loaf of white bread. Music played a large role in Ledermann's life from that time on. In 1928, when he was seventeen years old, Ledermann graduated from the Leibniz Gymnasium and entered the University of Berlin to study for the Staatsexamen, the qualification necessary to enter secondary school teaching.