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Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E
BOOK REVIEW Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E. Rowe Einstein’s Italian modern Italy. Nor does the author shy away from topics Mathematicians: like how Ricci developed his absolute differential calculus Ricci, Levi-Civita, and the as a generalization of E. B. Christoffel’s (1829–1900) work Birth of General Relativity on quadratic differential forms or why it served as a key By Judith R. Goodstein tool for Einstein in his efforts to generalize the special theory of relativity in order to incorporate gravitation. In This delightful little book re- like manner, she describes how Levi-Civita was able to sulted from the author’s long- give a clear geometric interpretation of curvature effects standing enchantment with Tul- in Einstein’s theory by appealing to his concept of parallel lio Levi-Civita (1873–1941), his displacement of vectors (see below). For these and other mentor Gregorio Ricci Curbastro topics, Goodstein draws on and cites a great deal of the (1853–1925), and the special AMS, 2018, 211 pp. 211 AMS, 2018, vast secondary literature produced in recent decades by the world that these and other Ital- “Einstein industry,” in particular the ongoing project that ian mathematicians occupied and helped to shape. The has produced the first 15 volumes of The Collected Papers importance of their work for Einstein’s general theory of of Albert Einstein [CPAE 1–15, 1987–2018]. relativity is one of the more celebrated topics in the history Her account proceeds in three parts spread out over of modern mathematical physics; this is told, for example, twelve chapters, the first seven of which cover episodes in [Pais 1982], the standard biography of Einstein. -
Lecture Notes for Felix Klein Lectures
Preprint typeset in JHEP style - HYPER VERSION Lecture Notes for Felix Klein Lectures Gregory W. Moore Abstract: These are lecture notes for a series of talks at the Hausdorff Mathematical Institute, Bonn, Oct. 1-11, 2012 December 5, 2012 Contents 1. Prologue 7 2. Lecture 1, Monday Oct. 1: Introduction: (2,0) Theory and Physical Mathematics 7 2.1 Quantum Field Theory 8 2.1.1 Extended QFT, defects, and bordism categories 9 2.1.2 Traditional Wilsonian Viewpoint 12 2.2 Compactification, Low Energy Limit, and Reduction 13 2.3 Relations between theories 15 3. Background material on superconformal and super-Poincar´ealgebras 18 3.1 Why study these? 18 3.2 Poincar´eand conformal symmetry 18 3.3 Super-Poincar´ealgebras 19 3.4 Superconformal algebras 20 3.5 Six-dimensional superconformal algebras 21 3.5.1 Some group theory 21 3.5.2 The (2, 0) superconformal algebra SC(M1,5|32) 23 3.6 d = 6 (2, 0) super-Poincar´e SP(M1,5|16) and the central charge extensions 24 3.7 Compactification and preserved supersymmetries 25 3.7.1 Emergent symmetries 26 3.7.2 Partial Topological Twisting 26 3.7.3 Embedded Four-dimensional = 2 algebras and defects 28 N 3.8 Unitary Representations of the (2, 0) algebra 29 3.9 List of topological twists of the (2, 0) algebra 29 4. Four-dimensional BPS States and (primitive) Wall-Crossing 30 4.1 The d = 4, = 2 super-Poincar´ealgebra SP(M1,3|8). 30 N 4.2 BPS particle representations of four-dimensional = 2 superpoincar´eal- N gebras 31 4.2.1 Particle representations 31 4.2.2 The half-hypermultiplet 33 4.2.3 Long representations 34 -
Pursuit of Genius: Flexner, Einstein, and the Early Faculty at the Institute
i i i i PURSUIT OF GENIUS i i i i i i i i PURSUIT OF GENIUS Flexner, Einstein,and the Early Faculty at the Institute for Advanced Study Steve Batterson Emory University A K Peters, Ltd. Natick, Massachusetts i i i i i i i i Editorial, Sales, and Customer Service Office A K Peters, Ltd. 5 Commonwealth Road, Suite 2C Natick, MA 01760 www.akpeters.com Copyright ⃝c 2006 by A K Peters, Ltd. All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopy- ing, recording, or by any information storage and retrieval system, without written permission from the copyright owner. Library of Congress Cataloging-in-Publication Data Batterson, Steve, 1950– Pursuit of genius : Flexner, Einstein, and the early faculty at the Institute for Advanced Study / Steve Batterson. p. cm. Includes bibliographical references and index. ISBN 13: 978-1-56881-259-5 (alk. paper) ISBN 10: 1-56881-259-0 (alk. paper) 1. Mathematics–Study and teaching (Higher)–New Jersey–Princeton–History. 2. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–History. 3. Institute for Advanced Study (Princeton, N.J.). School of Mathematics–Faculty. I Title. QA13.5.N383 I583 2006 510.7’0749652--dc22 2005057416 Cover Photographs: Front cover: Clockwise from upper left: Hermann Weyl (1930s, cour- tesy of Nina Weyl), James Alexander (from the Archives of the Institute for Advanced Study), Marston Morse (photo courtesy of the American Mathematical Society), Albert Einstein (1932, The New York Times), John von Neumann (courtesy of Marina von Neumann Whitman), Oswald Veblen (early 1930s, from the Archives of the Institute for Advanced Study). -
Felix Klein and His Erlanger Programm D
WDS'07 Proceedings of Contributed Papers, Part I, 251–256, 2007. ISBN 978-80-7378-023-4 © MATFYZPRESS Felix Klein and his Erlanger Programm D. Trkovsk´a Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. The present paper is dedicated to Felix Klein (1849–1925), one of the leading German mathematicians in the second half of the 19th century. It gives a brief account of his professional life. Some of his activities connected with the reform of mathematics teaching at German schools are mentioned as well. In the following text, we describe fundamental ideas of his Erlanger Programm in more detail. References containing selected papers relevant to this theme are attached. Introduction The Erlanger Programm plays an important role in the development of mathematics in the 19th century. It is the title of Klein’s famous lecture Vergleichende Betrachtungen ¨uber neuere geometrische Forschungen [A Comparative Review of Recent Researches in Geometry] which was presented on the occasion of his admission as a professor at the Philosophical Faculty of the University of Erlangen in October 1872. In this lecture, Felix Klein elucidated the importance of the term group for the classification of various geometries and presented his unified way of looking at various geometries. Klein’s basic idea is that each geometry can be characterized by a group of transformations which preserve elementary properties of the given geometry. Professional Life of Felix Klein Felix Klein was born on April 25, 1849 in D¨usseldorf,Prussia. Having finished his study at the grammar school in D¨usseldorf,he entered the University of Bonn in 1865 to study natural sciences. -
Open Research Online Oro.Open.Ac.Uk
Open Research Online The Open University’s repository of research publications and other research outputs The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective Conference or Workshop Item How to cite: Barrow-Green, June; Ponce Dawson, Silvina and Roy, Marie-Françoise (2019). The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective. In: Proceedings of the International Congress of Mathematicians - 2018 (Sirakov, Boyan; Ney de Souza, Paulo and Viana, Marcelo eds.), World Scientific, pp. 1073–1092. For guidance on citations see FAQs. c [not recorded] https://creativecommons.org/licenses/by-nc-nd/4.0/ Version: Accepted Manuscript Link(s) to article on publisher’s website: http://dx.doi.org/doi:10.1142/11060 Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online’s data policy on reuse of materials please consult the policies page. oro.open.ac.uk P. I. C. M. – 2018 Rio de Janeiro, Vol. (1073–1068) 1 THE GENDER GAP IN MATHEMATICAL AND NATURAL 2 SCIENCES FROM A HISTORICAL PERSPECTIVE 3 J B-G, S P D M-F R 4 5 Abstract 6 The panel organised by the Committee for Women in Mathematics (CWM) 7 of the International Mathematical Union (IMU) took place at the International nd 8 Congress of Mathematicians (ICM) on August 2 , 2018. It was attended by about 9 190 people, with a reasonable gender balance (1/4 men, 3/4 women). The panel was 10 moderated by Caroline Series, President of the London Mathematical Society and 11 Vice-Chair of CWM. -
ITS FIRST FIFTY YEARS Carl Β
THE MATHEMATICAL ASSOCIATION OF AMERICA: ITS FIRST FIFTY YEARS Carl Β. Boyer Brooklyn College, CUNY Richard W. Feldmann Lycoming College Harry M. Gehman SUN Yat Buffalo Phillip S. Jones University of Michigan Kenneth O. May University of Toronto Harriet F. Montague SUNYat Buffalo Gregory H. Moore University of Toronto Robert A. Rosenbaum Wesleyan University Emory P. Starke Rutgers University Dirk J. Struik Massachusetts Institute of Technology THE MATHEMATICAL ASSOCIATION OF AMERICA: ITS FIRST FIFTY YEARS Kenneth O. May, editor University of Toronto, Canada Published and distributed by The Mathematical Association of America Copyright 1972 by THE MATHEMATICAL ASSOCIATION OF AMERICA (INCORPORATED) PREFACE The fiftieth anniversary of the founding of the Mathematical Association of America was celebrated at the 1965 summer meeting at Cornell University [MONTHLY 72, 1053-1059]. The invited addresses on that occasion dealing with the past, present, and future of the Association and of mathematics, were published in the fiftieth anniversary issue [MONTHLY 74, Num. !, Part II] under the editorship of Carl B. Allendoerfer. The historical addresses by A. A. Bennett, R. A. Rosenbaum, W. L. Duren, Jr., and P. S. Jones whetted appetites for a more complete story of the Association. Early in 1966, on a recommendation of the Committee on Publications, President R. L. Wilder appointed a Committee on the Preparation of a Fifty-Year History of the Association consisting of Carl B. Boyer, Kenneth O. May (Chairman), and Dirk J. Struik. An appropriation of one thousand dollars was set aside to meet incidental expenses. The Committee began its work with very ambitious plans, hoping to get financial support for interviewing older members of the Association and the preparation of special studies on particular aspects of the Association's work. -
Sofia Kovalevskaya
Sofia Kovalevskaya Claire Larkin Kovalevskaya's life Sofia Kovalevskaya was born in Moscow, Russia on January 15th, 1850. She was born into a wealthy, well- educated family with an older sister and a younger brother. Sofia was often seen as the neglected middle child because both of her siblings were well-mannered and well-admired; she was always the odd one out. For these reasons, Sofia was not a happy child. She also had a governess who tried to make her into a young lady. However, Sofia always wanted to do math and science, subjects that were not acceptable for young women to do during that time period. One reason for her acquiring her interest in mathematics was her uncle, Pyotr Vasilievich Krukovsky, who spoke about the subject often in front of her. When she was 11, she grew a deep interest for the subject. She would study it on the wall of her nursery and then began studying it with a tutor. However, her father did not like the idea of his daughter doing math, so he put a stop to all of it. This forced her to learn math in the shadows of her family. Sofia was also extremely lucky that she lived next to Professor Tyrtov, a well known professor of mathematics and physics as well as author of a physics book Sofia read while she was young. Professor Tyrtov was beyond dumbfounded when he found out that Sofia had read and understood his book. He even claims that she understood and explained it in the same fashion that the founders of trigonometry did. -
An Outline of the History of Mathematics in the U
The Hilbert American Colony This file provides more biographical details on the Hilbert American colony than are given in the Transition_1900 section. Table 1 lists the 13 American students who earned doctorates under the direction of David Hilbert at Göttingen, in chronological order. Only one finished before the turn of the 20th century. One of the next two was Hilbert’s first female student. Rather than describing the lives and careers of the remaining eleven members of Hilbert’s American colony in chronological order, they appear according to their rankings published in the first three editions of American Men of Science (AMoS), which appeared in 1906, 1910 and 1921. In each of the three lists, scientists regarded as the most eminent in their field were asked to rank others in the field, with the top 1000 awarded stars beside their name. Eighty mathematicians were starred, and the numbers in the AMoS column in Table 1 designate the edition in which they were listed (if at all): 1 for 1906, 2 for 1910, and 3 for 1921. Name Year AMoS Legh Wilber Reid 1899 Anne Lucy Bosworth 1900 Edgar Jerome Townsend 1900 3 Earle Raymond Hedrick 1901 1, 2, 3 Charles Albert Noble 1901 Oliver Dimon Kellogg 1902 2, 3 Charles Max Mason 1903 2, 3 Wilhelmus David Westfall 1905 David Clinton Gillespie 1906 William DeWeese Cairns 1907 Arthur Robert Crathorne 1907 Charles Haseman 1907 Wallie Hurwitz 1910 3 Table 1: Hilbert’s American student Legh Wilber Reid (1867-1961) was the only American to complete requirements for a doctorate before 1900. -
Contributions to the History of Number Theory in the 20Th Century Author
Peter Roquette, Oberwolfach, March 2006 Peter Roquette Contributions to the History of Number Theory in the 20th Century Author: Peter Roquette Ruprecht-Karls-Universität Heidelberg Mathematisches Institut Im Neuenheimer Feld 288 69120 Heidelberg Germany E-mail: [email protected] 2010 Mathematics Subject Classification (primary; secondary): 01-02, 03-03, 11-03, 12-03 , 16-03, 20-03; 01A60, 01A70, 01A75, 11E04, 11E88, 11R18 11R37, 11U10 ISBN 978-3-03719-113-2 The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. 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, re-use of illustrations, recitation, broad- casting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2013 European Mathematical Society Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum SEW A27 CH-8092 Zürich Switzerland Phone: +41 (0)44 632 34 36 Email: [email protected] Homepage: www.ems-ph.org Typeset using the author’s TEX files: I. Zimmermann, Freiburg Printing and binding: Beltz Bad Langensalza GmbH, Bad Langensalza, Germany ∞ Printed on acid free paper 9 8 7 6 5 4 3 2 1 To my friend Günther Frei who introduced me to and kindled my interest in the history of number theory Preface This volume contains my articles on the history of number theory except those which are already included in my “Collected Papers”. -
Introduction
Notes Introduction 1 Marie Corelli, or Mary Mackay (1855–1924) was a successful romantic novelist. The quotation is from her pamphlet, Woman or – Suffragette? A Question of National Choice (London: C. Arthur Pearson, 1907). 2 Sally Ledger and Roger Luckhurst, eds, The Fin de Siècle: A Reader in Cultural History c.1880–1900 (Oxford: Oxford University Press, 2000), p. xii. 3 A central text is Steven Shapin and Simon Schaffer, Leviathan and the Air- pump: Hobbes, Boyle and the Experimental Life (Princeton: Princeton University Press, 1985). 4 Otto Mayr, ‘The science-technology relationship’, in Science in Context: Readings in the Sociology of Science, ed. by Barry Barnes and David Edge (Milton Keynes: Open University Press, 1982), pp. 155–163. 5 Nature, November 8 1900, News, p. 28. 6 For example Alison Winter, ‘A calculus of suffering: Ada Lovelace and the bodily constraints on women’s knowledge in early Victorian England’, in Science Incarnate: Historical Embodiments of Natural Knowledge, ed. by Christopher Lawrence and Steven Shapin (Chicago: University of Chicago Press, 1998), pp. 202–239 and Margaret Wertheim, Pythagoras’ Trousers: God, Physics and the Gender Wars (London: Fourth Estate, 1997). 7 Carl B. Boyer, A History of Mathematics (New York: Wiley, 1968), pp. 649–650. 8 For the social construction of mathematics see David Bloor, ‘Formal and informal thought’, in Science in Context: Readings in the Sociology of Science, ed. by Barry Barnes and David Edge (Milton Keynes: Open University Press, 1982), pp. 117–124; Math Worlds: Philosophical and Social Studies of Mathematics and Mathematics Education, ed. by Sal Restivo, Jean Paul Bendegem and Roland Fisher (Albany: State University of New York Press, 1993). -
S O C Z'atl'o N .Fo R Ome N I. Matics
s o c z'atl'on .fo r ome n i. matics Volume 13, Number 5 NEWSLETTE~ September-October 1983 **********--******************--*********** DU~| DUES! DUESI DUES! DUES| DUES| DuESI DDES| DUESI DUESI DuESI Du~| Dues are due October lo Please send them in along with your reminder postcard. Encourage your institution to become an institutiorml member (see the president Os report for more information). Consider becoming a contributing member yourself. MaRE ADDF~S CHANGESI AWMOs address is now A~, P.O. Box 178, Wellesley College, Wellesley, MA 02161. You may have noticed last issue that our president's address has also changed. See the end of the president's report for the new one. ******************************************* PRESIDENT iS REPORT Chan ~ institutional membershi So This year A~ is offering institutions the oppo ty spo~nsormemberships for students through a new category of membership called "Sponsoring Institutional Membership". For an extra $20 per year~ an institu- tion may name up to five (or for ~O, up to ten) students to become members of A~ and to receive this Newsletter. Current institutional members should have already received information about our new programj and prospective institutional members will hear from us soon. The purpose of the program is to introduce interested students to ANM through their departments. Boston Area grant. This stammer A~4 has been sponsoring a program which pays tuition for eligible women high school mathematics teachers who want to take courses in the computer language Pascal. The program has been made possible by a grant of $5000 from Raytheon. Eleanor Palais is chair of the A~ ~Ymdraising Committee. -
The Early Career of G.H. Hardy
THE EARLY CAREER OF G.H. HARDY by Brenda Davison B.A.Sc.(hons), University of British Columbia, 1989 a Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mathematics c Brenda Davison 2010 SIMON FRASER UNIVERSITY Summer 2010 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for Fair Dealing. Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. APPROVAL Name: Brenda Davison Degree: Master of Science Title of Thesis: The Early Career of G.H. Hardy Examining Committee: Dr. Veselin Jungić Chair Dr. W. Tom Archibald, Senior Supervisor Dr. Len Berggren, Supervisor Dr. Nilima Nigam, External Examiner Date Approved: ii Declaration of Partial Copyright Licence The author, whose copyright is declared on the title page of this work, has granted to Simon Fraser University the right to lend this thesis, project or extended essay to users of the Simon Fraser University Library, and to make partial or single copies only for such users or in response to a request from the library of any other university, or other educational institution, on its own behalf or for one of its users. The author has further granted permission to Simon Fraser University to keep or make a digital copy for use in its circulating collection (currently available to the public at the “Institutional Repository” link of the SFU Library website <www.lib.sfu.ca> at: <http://ir.lib.sfu.ca/handle/1892/112>) and, without changing the content, to translate the thesis/project or extended essays, if technically possible, to any medium or format for the purpose of preservation of the digital work.