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Commentary on the Kervaire–Milnor Correspondence 1958–1961
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 52, Number 4, October 2015, Pages 603–609 http://dx.doi.org/10.1090/bull/1508 Article electronically published on July 1, 2015 COMMENTARY ON THE KERVAIRE–MILNOR CORRESPONDENCE 1958–1961 ANDREW RANICKI AND CLAUDE WEBER Abstract. The extant letters exchanged between Kervaire and Milnor during their collaboration from 1958–1961 concerned their work on the classification of exotic spheres, culminating in their 1963 Annals of Mathematics paper. Michel Kervaire died in 2007; for an account of his life, see the obituary by Shalom Eliahou, Pierre de la Harpe, Jean-Claude Hausmann, and Claude We- ber in the September 2008 issue of the Notices of the American Mathematical Society. The letters were made public at the 2009 Kervaire Memorial Confer- ence in Geneva. Their publication in this issue of the Bulletin of the American Mathematical Society is preceded by our commentary on these letters, provid- ing some historical background. Letter 1. From Milnor, 22 August 1958 Kervaire and Milnor both attended the International Congress of Mathemati- cians held in Edinburgh, 14–21 August 1958. Milnor gave an invited half-hour talk on Bernoulli numbers, homotopy groups, and a theorem of Rohlin,andKer- vaire gave a talk in the short communications section on Non-parallelizability of the n-sphere for n>7 (see [2]). In this letter written immediately after the Congress, Milnor invites Kervaire to join him in writing up the lecture he gave at the Con- gress. The joint paper appeared in the Proceedings of the ICM as [10]. Milnor’s name is listed first (contrary to the tradition in mathematics) since it was he who was invited to deliver a talk. -
George W. Whitehead Jr
George W. Whitehead Jr. 1918–2004 A Biographical Memoir by Haynes R. Miller ©2015 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. GEORGE WILLIAM WHITEHEAD JR. August 2, 1918–April 12 , 2004 Elected to the NAS, 1972 Life George William Whitehead, Jr., was born in Bloomington, Ill., on August 2, 1918. Little is known about his family or early life. Whitehead received a BA from the University of Chicago in 1937, and continued at Chicago as a graduate student. The Chicago Mathematics Department was somewhat ingrown at that time, dominated by L. E. Dickson and Gilbert Bliss and exhibiting “a certain narrowness of focus: the calculus of variations, projective differential geometry, algebra and number theory were the main topics of interest.”1 It is possible that Whitehead’s interest in topology was stimulated by Saunders Mac Lane, who By Haynes R. Miller spent the 1937–38 academic year at the University of Chicago and was then in the early stages of his shift of interest from logic and algebra to topology. Of greater importance for Whitehead was the appearance of Norman Steenrod in Chicago. Steenrod had been attracted to topology by Raymond Wilder at the University of Michigan, received a PhD under Solomon Lefschetz in 1936, and remained at Princeton as an Instructor for another three years. He then served as an Assistant Professor at the University of Chicago between 1939 and 1942 (at which point he moved to the University of Michigan). -
Millennium Prize for the Poincaré
FOR IMMEDIATE RELEASE • March 18, 2010 Press contact: James Carlson: [email protected]; 617-852-7490 See also the Clay Mathematics Institute website: • The Poincaré conjecture and Dr. Perelmanʼs work: http://www.claymath.org/poincare • The Millennium Prizes: http://www.claymath.org/millennium/ • Full text: http://www.claymath.org/poincare/millenniumprize.pdf First Clay Mathematics Institute Millennium Prize Announced Today Prize for Resolution of the Poincaré Conjecture a Awarded to Dr. Grigoriy Perelman The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. The citation for the award reads: The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman. The Poincaré conjecture is one of the seven Millennium Prize Problems established by CMI in 2000. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude. The award of the Millennium Prize to Dr. Perelman was made in accord with their governing rules: recommendation first by a Special Advisory Committee (Simon Donaldson, David Gabai, Mikhail Gromov, Terence Tao, and Andrew Wiles), then by the CMI Scientific Advisory Board (James Carlson, Simon Donaldson, Gregory Margulis, Richard Melrose, Yum-Tong Siu, and Andrew Wiles), with final decision by the Board of Directors (Landon T. -
August 1995 Council Minutes
AMERICAN MATHEMATICAL SOCIETY COUNCIL MINUTES Burlington, Vermont 05 August 1995 Abstract The Council of the American Mathematical Society met at 1:00 p.m. on Satur- day, 05 August 1995, in the Emerald Grand Ballroom in the Sheraton Burlington, Burlington, Vermont. These are the minutes for the meeting. Members present were Georgia Benkart, Joan Birman, Robert Daverman (vot- ing Associate Secretary), David Epstein, Robert Fossum, John Franks, Ron Gra- ham, Steven Krantz, Andy Magid (Associate Secretary), Cathleen Morawetz, Frank Morgan, Franklin Peterson, Marc Rieffel, Cora Sadosky, Norberto Salinas, Peter Shalen, Lesley Sibner (Associate Secretary), B. A. Taylor, Jean Taylor, and Sylvia Wiegand. Staff and others invited to attend were Don Babbitt (Publisher), Annalisa Cran- nell (Committee on the Profession Representative), Chandler Davis (Canadian Mathematical Society Representative), John Ewing (Executive Director), Tim Gog- gins (Development Officer), Carolyn Gordon (Editorial Boards Committee Repre- sentative), Jim Lewis (Committee on Science Policy Chair), James Maxwell (AED), Don McClure (Trustee), Susan Montgomery (Trustee), Everett Pitcher (Former Secretary), Sam Rankin (AED), and Kelly Young (Assistant to the Secretary). President Morawetz presided. 1 2 CONTENTS Contents IAGENDA 4 0 CALL TO ORDER AND INTRODUCTIONS. 4 1MINUTES 4 1.1March95Council...................................... 4 1.2 05/95 Meeting of the Executive Committee and Board of Trustees. 4 2 CONSENT AGENDA. 4 2.1Resolutions......................................... 4 2.1.1 Exxon Foundation. ......................... 4 2.2CommitteeAdministration................................ 5 2.2.1 Dischargewiththanks............................... 5 2.2.2 CommitteeCharges................................ 5 3 REPORTS OF BOARDS AND STANDING COMMITTEES. 5 3.1 EDITORIAL BOARDS COMMITTEE (EBC). .................. 5 3.1.1 TransactionsandMemoirsEditorialCommittee................. 5 3.1.2 Journal of the AMS . -
Harmonic Analysis and Partial Differential Equations
AMERICAN MATHEMATICAL SOCIETY 107 Harmonic Analysis and Partial Differential Equations Proceedings of a Conference held April 4-5, 1988 http://dx.doi.org/10.1090/conm/107 Titles in This Series Volume 1 Markov random fields and their 19 Proceedings of the Northwestern applications, Ross Kindermann and homotopy theory conference, Haynes J. Laurie Snell R. Miller and Stewart B. Priddy, Editors 2 Proceedings of the conference on 20 Low dimensional topology, Samuel J. integration, topology, and geometry in Lomonaco, Jr., Editor linear spaces, William H. Graves, Editor 21 Topological methods in nonlinear 3 The closed graph and P-closed functional analysis, S. P. Singh, graph properties in general topology, S. Thomaier, and B. Watson, Editors T. R. Hamlett and L. L. Herrington 22 Factorizations of b" ± 1, b = 2, 4 Problems of elastic stability and 3, 5, 6, 7, 10, 11, 12 up to high vibrations, Vadim Komkov, Editor powers, John Brillhart, D. H. Lehmer, 5 Rational constructions of modules J. L. Selfridge, Bryant Tuckerman, and for simple Lie algebras, George B. S. S. Wagstaff, Jr. Seligman 23 Chapter 9 of Ramanujan's second 6 Umbral calculus and Hopf algebras, notebook-Infinite series identities, Robert Morris, Editor transformations, and evaluations, Bruce C. Berndt and Padmini T. Joshi 7 Complex contour integral representation of cardinal spline 24 Central extensions, Galois groups, and functions, Walter Schempp ideal class groups of number fields, A. Frohlich 8 Ordered fields and real algebraic geometry, D. W. Dubois and T. Recio, 25 Value distribution theory and its Editors applications, Chung-Chun Yang, Editor 9 Papers in algebra, analysis and 26 Conference in modern analysis statistics, R. -
The Arf-Kervaire Invariant Problem in Algebraic Topology: Introduction
THE ARF-KERVAIRE INVARIANT PROBLEM IN ALGEBRAIC TOPOLOGY: INTRODUCTION MICHAEL A. HILL, MICHAEL J. HOPKINS, AND DOUGLAS C. RAVENEL ABSTRACT. This paper gives the history and background of one of the oldest problems in algebraic topology, along with a short summary of our solution to it and a description of some of the tools we use. More details of the proof are provided in our second paper in this volume, The Arf-Kervaire invariant problem in algebraic topology: Sketch of the proof. A rigorous account can be found in our preprint The non-existence of elements of Kervaire invariant one on the arXiv and on the third author’s home page. The latter also has numerous links to related papers and talks we have given on the subject since announcing our result in April, 2009. CONTENTS 1. Background and history 3 1.1. Pontryagin’s early work on homotopy groups of spheres 3 1.2. Our main result 8 1.3. The manifold formulation 8 1.4. The unstable formulation 12 1.5. Questions raised by our theorem 14 2. Our strategy 14 2.1. Ingredients of the proof 14 2.2. The spectrum Ω 15 2.3. How we construct Ω 15 3. Some classical algebraic topology. 15 3.1. Fibrations 15 3.2. Cofibrations 18 3.3. Eilenberg-Mac Lane spaces and cohomology operations 18 3.4. The Steenrod algebra. 19 3.5. Milnor’s formulation 20 3.6. Serre’s method of computing homotopy groups 21 3.7. The Adams spectral sequence 21 4. Spectra and equivariant spectra 23 4.1. -
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. -
Polish Mathematicians and Mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire)
Science in Poland Stanisław Domoradzki ORCID 0000-0002-6511-0812 Faculty of Mathematics and Natural Sciences, University of Rzeszów (Rzeszów, Poland) [email protected] Małgorzata Stawiska ORCID 0000-0001-5704-7270 Mathematical Reviews (Ann Arbor, USA) [email protected] Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire) Abstract In this article we present diverse experiences of Polish math- ematicians (in a broad sense) who during World War I fought for freedom of their homeland or conducted their research and teaching in difficult wartime circumstances. We discuss not only individual fates, but also organizational efforts of many kinds (teaching at the academic level outside traditional institutions, Polish scientific societies, publishing activities) in order to illus- trate the formation of modern Polish mathematical community. PUBLICATION e-ISSN 2543-702X INFO ISSN 2451-3202 DIAMOND OPEN ACCESS CITATION Domoradzki, Stanisław; Stawiska, Małgorzata 2018: Polish mathematicians and mathematics in World War I. Part I: Galicia (Austro-Hungarian Empire. Studia Historiae Scientiarum 17, pp. 23–49. Available online: https://doi.org/10.4467/2543702XSHS.18.003.9323. ARCHIVE RECEIVED: 2.02.2018 LICENSE POLICY ACCEPTED: 22.10.2018 Green SHERPA / PUBLISHED ONLINE: 12.12.2018 RoMEO Colour WWW http://www.ejournals.eu/sj/index.php/SHS/; http://pau.krakow.pl/Studia-Historiae-Scientiarum/ Stanisław Domoradzki, Małgorzata Stawiska Polish mathematicians and mathematics in World War I ... In Part I we focus on mathematicians affiliated with the ex- isting Polish institutions of higher education: Universities in Lwów in Kraków and the Polytechnical School in Lwów, within the Austro-Hungarian empire. -
Matical Society Was Held at Columbia University on Friday and Saturday, April 25-26, 1947
THE APRIL MEETING IN NEW YORK The four hundred twenty-fourth meeting of the American Mathe matical Society was held at Columbia University on Friday and Saturday, April 25-26, 1947. The attendance was over 300, includ ing the following 300 members of the Society: C. R. Adams, C. F. Adler, R. P. Agnew, E.J. Akutowicz, Leonidas Alaoglu, T. W. Anderson, C. B. Allendoerfer, R. G. Archibald, L. A. Aroian, M. C. Ayer, R. A. Bari, Joshua Barlaz, P. T. Bateman, G. E. Bates, M. F. Becker, E. G. Begle, Richard Bellman, Stefan Bergman, Arthur Bernstein, Felix Bernstein, Lipman Bers, D. H. Blackwell, Gertrude Blanch, J. H. Blau, R. P. Boas, H. W. Bode, G. L. Bolton, Samuel Borofsky, J. M. Boyer, A. D. Bradley, H. W. Brinkmann, Paul Brock, A. B. Brown, G. W. Brown, R. H. Brown, E. F. Buck, R. C. Buck, L. H. Bunyan, R. S. Burington, J. C. Burkill, Herbert Busemann, K. A. Bush, Hobart Bushey, J. H. Bushey, K. E. Butcher, Albert Cahn, S. S. Cairns, W. R. Callahan, H. H. Campaigne, K. Chandrasekharan, J. O. Chellevold, Herman Chernoff, Claude Chevalley, Ed mund Churchill, J. A. Clarkson, M. D. Clement, R. M. Cohn, I. S. Cohen, Nancy Cole, T. F. Cope, Richard Courant, M. J. Cox, F. G. Critchlow, H. B. Curry, J. H. Curtiss, M. D. Darkow, A. S. Day, S. P. Diliberto, J. L. Doob, C. H. Dowker, Y. N. Dowker, William H. Durf ee, Churchill Eisenhart, Benjamin Epstein, Ky Fan, J.M.Feld, William Feller, F. G. Fender, A. D. -
Elkin, Judith Laikin. "Jews and Non-Jews. " the Jews of Latin America. Rev. Ed. New York
THE JEWS OF LATIN AMERICA Revised Edition JUDITH LAIKIN ELKIN HOLMES & MEIER NEW YORK / LONDON Published in the United Stutes of America 1998 b y ll olmes & Meier Publishers. Inc . 160 Broadway ew York, NY 10038 Copyr ight © 199 by Holmes & Meier Publishers, 1.nc. F'irst edition published und er th e title Jeics of the u1tl11A111erica11 lle1'11hlics copyright © 1980 The University of o rth Ca rolina Press . Chapel Hill , NC . All rights reserved . No part of this book may be reproduced or transmitted in any form or by any elec troni c o r mechanical means now known or to be invented, including photocopying , r co rdin g, and information storage and retrieval systems , without permission in writing from the publishers , exc·ept by a reviewe r who may quote brief passages in a review. The auth or acknow ledges with gra titud e the court esy of the American Jewish lli stori cal Society to reprint the follo,ving articl e which is published in somewhat different form in this book: "Goo dnight , Sweet Gaucho: A Revisio nist View of the Jewis h Agricultural Experiment in Argentina, " A111eric1111j etds h Historic(I/ Q11111terly67 (March 1978 ): 208 - 23. Most of the photographs in this boo k were includ d in the exhibit ion . "Voyages to F're dam: .500 Years of Je,vish Li~ in Latin America and the Caribbean ," and were ma de availab le throu ,I, the court esy of the Anti-Defamation League of B'nai B'rith . Th e two photographs of the AMIA on pages 266 - 267 we re s uppli ed by the AMIA -Co munidad Judfa de Buenos Aires. -
Notices of the American Mathematical Society
OF THE 1994 AMS Election Special Section page 7 4 7 Fields Medals and Nevanlinna Prize Awarded at ICM-94 page 763 SEPTEMBER 1994, VOLUME 41, NUMBER 7 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe· January 1994 issue of the Notices on page 43. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island, on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings Abstract Program Meeting# Date Place Deadline Issue 895 t October 28-29, 1994 Stillwater, Oklahoma Expired October 896 t November 11-13, 1994 Richmond, Virginia Expired October 897 * January 4-7, 1995 (101st Annual Meeting) San Francisco, California October 3 January 898 * March 4-5, 1995 Hartford, Connecticut December 1 March 899 * March 17-18, 1995 Orlando, Florida December 1 March 900 * March 24-25, -
Math Student 2007
ISSN: 0025-5742 THE MATHEMATICS STUDENT Volume 76, Numbers 1 - 4, (2007) copy- Edited by J. R. PATADIA circulation (Issued: October, 2008) Member'sfor not PUBLISHED BY THE INDIAN MATHEMATICAL SOCIETY (In the memory of late Professor M. K. Singal) THE MATHEMATICS STUDENT Edited by J. R. PATADIA In keeping with the current periodical policy, THE MATHEMATICS STUDENT (STUDENT) will seek to publish material of interest not just to mathematicians with specialized interest but to undergraduate and postgraduate students and teachers of mathematics in India. With this in view, it will publish material of the following type: 1. Expository articles and popular (not highly technical) articles. 2. Classroom notes (this can include hints on teaching certain topics or filling vital gaps in the usual treatments of topics to be found in text-books or how some execises can and should be made an integral part of teaching, etc.) 3. Problems and solutions, News and Views. 4. Information on articles of common interest published in other periodicals, 5. Proceedings of IMS Conferences. Expository articles, classroom notes, news and announcements and research papers are invited for publication in THE MATHEMATICS STUDENT. Manuscripts intended for publication should preferably be submitted online in the LaTeX .pdf file or in the standard word processing format (Word or Word Perfect) including figures and tables. In case of hard copy submission, three copies of the manuscripts along with the Compact Disc (CD) copy should be submitted to the Editor Dr. J. R. Patadia, Department of Mathematics, faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002 (Gujarat),copy- India.