DOCSLIB.ORG

Maverick Mathematician: the Life and Science of J.E. Moyal

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Maverick Mathematician: the Life and Science of J.E. Moyal MAVERICK MATHEMATICIAN The Life and Science of J.E. Moyal MAVERICK MATHEMATICIAN The Life and Science of J.E. Moyal Ann Moyal Published by ANU E Press The Australian National University Canberra ACT 0200, Australia Email: [email protected] Web: http://epress.anu.edu.au National Library of Australia Cataloguing-in-Publication entry Moyal, Ann (Ann Mozley), 1926- . Maverick mathematician : the life and science of J.E. Moyal. Includes index. ISBN 1 920942 58 0 (pbk). ISBN 1 920942 59 9 (online) 1. Moyal, J. E. 2. Dirac, P. A. M. (Paul Adrien Maurice), 1902- - Correspondence. 3. Mathematicians - Australia - Biography. 4. Aerospace engineers - Australia - Biography. 5. Quantum theory - Mathematics. I. Title. 510.92 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of the publisher. Indexed by Dr Ann Moyal. Cover design by Teresa Prowse. Portrait by Linda Phillips, 1992. This edition © 2006 ANU E Press To Mimi Hurley, my sister and J.E.M.’s friend. Table of Contents Acknowledgements vii Preface xi Chapter 1. Boyhood 1 Chapter 2. The Making of a Scientific Maverick 9 Chapter 3. Battle With a Legend 19 Chapter 4. The Widening Circle 45 Chapter 5. Antipodean Winds 61 Chapter 6. Argonne National Laboratory 79 Chapter 7. Macquarie University 91 Chapter 8. The Reflective Years 103 Appendix I. Publications of J.E. Moyal 119 Appendix II. P.A.M. Dirac – J. E. Moyal: Correspondence, 1944-1946. Basser Library, Australian Academy of Science, Canberra, MS 45/3/ 123 Appendix III. Quantum Mechanics as a Statistical Theory by J.E. Moyal 163 Index 191 List of Figures 1.1. Palestine under the British Mandate 1922±1948 2 3.1. Paul Dirac, tenacious `high priest' of theoretical physics 22 3.2. Letter from P.A.M. Dirac 35 4.1. Maurice Bartlett, statistician ± a valuable ally and colleague of Joe's 45 4.2. Harry Messel, Sydney University's dynamic director of the School of Physics until 1987 56 5.1. The young Australian National University in 1958 where staff, recruited across many disciplines, mixed in the temporary structure of the `Old Hospital Building' seen here 61 5.2. JM Ð in Canberra, 1958. Appointed Reader in Statistics at the ANU that year, he was an early founding scientist of the University 66 5.3. Ann Mozley arrived at the ANU late in 1958 to help found the Australian Dictionary of Biography 71 5.4. Statistician Joe Gani took up a position in the Department of Statistics, ANU in 1961 72 5.5. Joe Moyal after his marriage to Ann, 1963 74 6.1. Argonne National Laboratory, America's leading National Atomic Energy Laboratory for peaceful purposes. Deer played in its spacious parks 79 6.2. JM Ð with familiar cigar at the Moyal apartment, Lisle, Illinois 82 6.3. Joe ready to dive in Caribbean waters, 1969 84 7.1. John Clive Ward, an eminent figure in physics at Macquarie 93 7.2. Macquarie mathematician, Alan McIntosh, who would rise to become head of the Centre for Mathematics and its Applications at the ANU 96 8.1. Joe Moyal in retirement, still thinking about quantum theory 103 8.2. Joe camping in Queensland, 1984 114 8.3. Portrait of Ann and Joe Moyal, Canberra, 1995 116 vi Maverick Mathematician Acknowledgements This small book could not have been written without the very considerable, and most generous, help of many people. My greatest debt is to several distinguished scientists Ð mathematicians and physicists Ð who have helped me chart a route through my late husband's scientific writings and who have added important evaluations and interpretative commentary to the text. Hence, in the best sense, several parts of this book have become `polyvocal'. The impulse towards this arises from the fact that, while I have practised for several decades as an historian of science, technology and telecommunications, with a particular emphasis on Australian science, I have had no previous training in the physical sciences. Writing this book has added an unanticipated dimension to my scientific interests and understanding. At the same time it has opened up, via email and the Internet, some highly rewarding international contacts and communication. My first and very real debt is to Professor Alan McIntosh of The Australian National University who, as a former junior colleague and friend of Joe Moyal during his final career years at Macquarie University in Sydney, has guided me to important sources and researchers, carefully read several draft chapters, and provided quiet, professional, and encouraging advice. I also owe an enormous debt of gratitude to Dr Cosmas Zachos of the High Energy Physics Division of Argonne National Laboratory, Illinois, USA, who has long had an intimate knowledge of the classic Moyal paper of 1949, `Quantum Mechanics as a Statistical Theory', and has, through detailed and quickening email correspondence, given me the benefit of his knowledgeable insights into phase space quantum mechanics and the Dirac-Moyal Correspondence of 1944±46 which, in Appendix II, forms an important part of this biography. His communications, delivered with allusive clarity and engaging literary eloquence, have given me much pleasure. Sight unseen, he has proved a most rewarding friend. Professor Thomas Curtright of the Department of Physics at Miami University, co-author with Dr Zachos (and David B. Fairlie) of Quantum vii Mechanics in Phase Space. An Overview with Selected Papers (2005)1 , has also given me thoughtful and illuminating recommendations and important encouragement. My warm thanks are also due to the three international colleagues Ð Dr Bruno Iochum of the Centre of Theoretical Physics and the University of Provence, Marseilles; Professor Joseph Várilly of the Department of Mathematics at the University of Costa Rica, San Jose, and Professor José Gracia-Bondia of the Department of Theoretical Physics at the University of Complutense, Madrid Ð for their generous contribution to the final chapter of this book relating to their diverse collaborative work which drew upon J.E. Moyal's early quantum research. Professor John Klauder of the Department of Physics and Mathematics, University of Florida, Miami has also granted me permission to quote from his commentary on Joe Moyal's mathematical contribution to quantum mechanics. In Australia I have received great assistance from the distinguished statistician, Emeritus Professor Joe Gani of The Australian National University, a very old friend and colleague of Joe Moyal, who, both in personal communication and through his writings, has furnished valuable material for this book. I have also been the recipient of enlightening insights and support from Professor Alan Carey, Director of the Centre for Mathematics and its Applications at the ANU. Emeritus Professor Harry Messel from the Department of Physics at the University of Sydney has provided his lively and warm recollections. From Macquarie University, Dr John Corbett has supported this endeavour with his pertinent observations and reflections; Professor Don McNeil in Statistics, and Professors Ross Street and William Chen in Mathematics have been helpful communicators and encouragers; while David Forrester, a former mature-age student in the Department of Mathematics, has provided some spirited and informative communication. From the University of Queensland, physicist Professor Tony Bracken has responded with helpful interest to my enquiries. In addition, Chris Weatherall, Colin Steele, and Hilary Webster have contributed in viii Maverick Mathematician different ways to the life of the book. I thank them all most warmly for their assistance. Various institutional libraries and archives have provided relevant documents for the research. These include the Basser Library of the Australian Academy of Science, Canberra, which holds the Dirac-Moyal Correspondence; the University Archives of The Australian National University, and Macquarie University Records and Archives Services. My personal thanks are also due to Dr Margaret Butler and Laboratory Historian, Catherine Westfall, at Argonne National Laboratory, Illinois, for their helpful record searches. Importantly, The Australian National University Library has afforded me access to its resources and to its specialized websites for the conduct of this research. I also extend my grateful thanks to Sue Kosse, Paul McNamara and Arvind Kalia for their continuing assistance, and as always, the Petherick Room of the National Library of Australia has provided a welcoming scholarly hearth. In addition, I owe particular thanks to Vic Elliott and Lorena Kanellopoulos at ANU E Press for their imaginative contribution to this volume. Finally this book would never have been brought together without the patient and good-humoured assistance of my godson, Angus Rea of Sydney, who has guided me through the ever-present pitfalls of sophisticated computer technology. ENDNOTE 1 World Scientific Series in 20th Century Physics, vol. 34, World Scientific, New Jersey, 2005. Acknowledgements ix Preface There is currently a recognition of the importance of the stories of individual scientists (outside the pantheon of giants and leading discipline figures) in building the history of science. Such individuals are unique men and women of outstanding ability, drawn from different countries and backgrounds, some of whose personal trajectories may move outside the practices and paradigms of established disciplines, and who, as researchers and experimenters, can prove to be significantly ahead of their time. This recognition has also derived from the fact that, in addition to the traditional theme of the great men of science, another trend has developed in the writing of the history of science in the last two decades Ð that of a strong focus on science in its social context, on the constructed nature of scientific knowledge and on a sociological emphasis that has tended to edge out the creative, individual, self-determining life in science.
Load more

Recommended publications
  • To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology?
    Portland State University PDXScholar Young Historians Conference Young Historians Conference 2016 Apr 28th, 9:00 AM - 10:15 AM To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology? Hayley A. LeBlanc Sunset High School Follow this and additional works at: https://pdxscholar.library.pdx.edu/younghistorians Part of the European History Commons, and the History of Science, Technology, and Medicine Commons Let us know how access to this document benefits ou.y LeBlanc, Hayley A., "To What Extent Did British Advancements in Cryptanalysis During World War II Influence the Development of Computer Technology?" (2016). Young Historians Conference. 1. https://pdxscholar.library.pdx.edu/younghistorians/2016/oralpres/1 This Event is brought to you for free and open access. It has been accepted for inclusion in Young Historians Conference by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. To what extent did British advancements in cryptanalysis during World War 2 influence the development of computer technology? Hayley LeBlanc 1936 words 1 Table of Contents Section A: Plan of Investigation…………………………………………………………………..3 Section B: Summary of Evidence………………………………………………………………....4 Section C: Evaluation of Sources…………………………………………………………………6 Section D: Analysis………………………………………………………………………………..7 Section E: Conclusion……………………………………………………………………………10 Section F: List of Sources………………………………………………………………………..11 Appendix A: Explanation of the Enigma Machine……………………………………….……...13 Appendix B: Glossary of Cryptology Terms.…………………………………………………....16 2 Section A: Plan of Investigation This investigation will focus on the advancements made in the field of computing by British codebreakers working on German ciphers during World War 2 (1939­1945).
    [Show full text]
  • Infinitely Many Star Products to Play With
    DSF{40{01 BiBoS 01-12-068 ESI 1109 hep{th/0112092 December 2001 Infinitely many star products to play with J.M. Gracia-Bond´ıa a;b, F. Lizzi b, G. Marmo b and P. Vitale c a BiBoS, Fakult¨atder Physik, Universit¨atBielefeld, 33615 Bielefeld, Germany b Dipartimento di Scienze Fisiche, Universit`adi Napoli Federico II and INFN, Sezione di Napoli, Monte S. Angelo Via Cintia, 80126 Napoli, Italy [email protected], [email protected] c Dipartimento di Fisica, Universit`adi Salerno and INFN Gruppo Collegato di Salerno, Via S. Allende 84081 Baronissi (SA), Italy [email protected] Abstract While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [xi; xj] = iθij. Here we present new classes of (non-formal) deformed products k associated to linear Lie algebras of the kind [xi; xj] = icijxk. For all possible three- dimensional cases, we define a new star product and discuss its properties. To complete the analysis of these novel noncommutative spaces, we introduce noncom- pact spectral triples, and the concept of star triple, a specialization of the spectral triple to deformations of the algebra of functions on a noncompact manifold. We examine the generalization to the noncompact case of Connes' conditions for non- commutative spin geometries, and, in the framework of the new star products, we exhibit some candidates for a Dirac operator. On the technical level, properties of 2n the Moyal multiplier algebra M(Rθ ) are elucidated. 1 Introduction Over five years ago, Connes gave the first axiomatics for first-quantized fermion fields on (compact) noncommutative varieties, the so-called spectral triples [1].
    [Show full text]
  • Homage to Gaia
    Homage to Gaia The Life of an Independent Scientist James Lovelock Souvenir Press I dedicate this book to my beloved wife Sandy This paperback published in 2019 First published by Souvenir Press in 2014, an imprint of Profile Books Ltd 3 Holford Yard Bevin Way London WC1X 9HD www.profilebooks.com First published in Great Britain in 2000 by Oxford University Press Copyright © 2000, 2013 by J.E. Lovelock Copyright © 2000, 2013, 2019 by J. E. Lovelock First published in 2000 by Oxford University Press The right of James Lovelock to be identified as the author of this work has been Thisasserted second in accordance paperback withedition section published 77 of thein 2014 Copyright, by Souvenir Designs Press and Ltd Patents Act, 431988 Great Russell Street, London WC1B 3PD All rights reserved. No part of this publication may be reproduced, stored in a Theretrieval right system of James or Lovelocktransmitted, to be in identifiedany form oras bythe any means, electronic, mechanical, authorphotocopying, of this work or otherwise, has been withoutasserted the in accordanceprior permission with of the Copyright owner. section 77 of the Copyright, Designs and Patents Act, 1988 ISBN 978 1 78816 460 3 All rights reserved. No part of this publication may be reproduced, eISBN 978 0 28564 256 0 stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, withoutPrinted andthe priorbound permission in Great Britain of the byCopyright owner. CPI Group (UK) Ltd, Croydon, CRO 4YY ISBN 9780285642553 Offset from the Oxford University Press edition of ‘Homage to Gaia: The Life of an Independent Scientist’ by James Lovelock.
    [Show full text]
  • Mothers in Science
    The aim of this book is to illustrate, graphically, that it is perfectly possible to combine a successful and fulfilling career in research science with motherhood, and that there are no rules about how to do this. On each page you will find a timeline showing on one side, the career path of a research group leader in academic science, and on the other side, important events in her family life. Each contributor has also provided a brief text about their research and about how they have combined their career and family commitments. This project was funded by a Rosalind Franklin Award from the Royal Society 1 Foreword It is well known that women are under-represented in careers in These rules are part of a much wider mythology among scientists of science. In academia, considerable attention has been focused on the both genders at the PhD and post-doctoral stages in their careers. paucity of women at lecturer level, and the even more lamentable The myths bubble up from the combination of two aspects of the state of affairs at more senior levels. The academic career path has academic science environment. First, a quick look at the numbers a long apprenticeship. Typically there is an undergraduate degree, immediately shows that there are far fewer lectureship positions followed by a PhD, then some post-doctoral research contracts and than qualified candidates to fill them. Second, the mentors of early research fellowships, and then finally a more stable lectureship or career researchers are academic scientists who have successfully permanent research leader position, with promotion on up the made the transition to lectureships and beyond.
    [Show full text]
  • Branched Hamiltonians and Supersymmetry
    Branched Hamiltonians and Supersymmetry Thomas Curtright, University of Miami Wigner 111 seminar, 12 November 2013 Some examples of branched Hamiltonians are explored, as recently advo- cated by Shapere and Wilczek. These are actually cases of switchback poten- tials, albeit in momentum space, as previously analyzed for quasi-Hamiltonian dynamical systems in a classical context. A basic model, with a pair of Hamiltonian branches related by supersymmetry, is considered as an inter- esting illustration, and as stimulation. “It is quite possible ... we may discover that in nature the relation of past and future is so intimate ... that no simple representation of a present may exist.” – R P Feynman Based on work with Cosmas Zachos, Argonne National Laboratory Introduction to the problem In quantum mechanics H = p2 + V (x) (1) is neither more nor less difficult than H = x2 + V (p) (2) by reason of x, p duality, i.e. the Fourier transform: ψ (x) φ (p) ⎫ ⎧ x ⎪ ⎪ +i∂/∂p ⎪ ⇐⇒ ⎪ ⎬⎪ ⎨⎪ i∂/∂x p − ⎪ ⎪ ⎪ ⎪ ⎭⎪ ⎩⎪ This equivalence of (1) and (2) is manifest in the QMPS formalism, as initiated by Wigner (1932), 1 2ipy/ f (x, p)= dy x + y ρ x y e− π | | − 1 = dk p + k ρ p k e2ixk/ π | | − where x and p are on an equal footing, and where even more general H (x, p) can be considered. See CZ to follow, and other talks at this conference. Or even better, in addition to the excellent books cited at the conclusion of Professor Schleich’s talk yesterday morning, please see our new book on the subject ... Even in classical Hamiltonian mechanics, (1) and (2) are equivalent under a classical canonical transformation on phase space: (x, p) (p, x) ⇐⇒ − But upon transitioning to Lagrangian mechanics, the equivalence between the two theories becomes obscure.
    [Show full text]
  • Phase Space Quantum Mechanics Is Such a Natural Formulation of Quantum Theory
    Phase space quantum mechanics Maciej B laszak, Ziemowit Doma´nski Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Pozna´n, Poland Abstract The paper develope the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise prod- uct of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket is the key element in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special cases all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental then the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism.
    [Show full text]
  • National Life Stories an Oral History of British Science
    NATIONAL LIFE STORIES AN ORAL HISTORY OF BRITISH SCIENCE Professor Michael McIntyre Interviewed by Paul Merchant C1379/72 Please refer to the Oral History curators at the British Library prior to any publication or broadcast from this document. Oral History The British Library 96 Euston Road London NW1 2DB United Kingdom +44 (0)20 7412 7404 [email protected] Every effort is made to ensure the accuracy of this transcript, however no transcript is an exact translation of the spoken word, and this document is intended to be a guide to the original recording, not replace it. Should you find any errors please inform the Oral History curators The British Library National Life Stories Interview Summary Sheet Title Page Ref no: C1379/72 Collection title: An Oral History of British Science Interviewee’s surname: McIntyre Title: Professor Interviewee’s forename: Michael Sex: Male Occupation: Applied Date and place of birth: 28/7/1941, Sydney, mathematician Australia Mother’s occupation: / Father’s occupation: Neurophysiologist Dates of recording, tracks (from – to): 28/03/12 (track 1-3), 29/03/12 (track 4-6), 30/03/12 (track 7-8) Location of interview: Department of Applied Mathematics and Theoretical Physics, University of Cambridge Name of interviewer: Dr Paul Merchant Type of recorder: Marantz PMD661 Recording format : WAV 24 bit 48kHz Total no. of tracks: 8 Mono/Stereo: Stereo Total Duration: 9:03:31 Additional material: The interview transcripts for McIntyre’s mother, Anne, father, Archibald Keverall and aunt, Anne Edgeworth are available for public access. Please contact the oral history section for more details.
    [Show full text]
  • De Morgan Newsletter 2008
    UCL DEPARTMENT OF MATHEMATICS DDee MMoorrggaann AAssssoocciiaattiioonn NNeewwsslleetttteerr from the Department of Mathematics UCL Issue - 16 - 2008 Editor - Michael O'Neill De Morgan Association Dinner Wednesday 4 June 2008 The venue for the Annual Dinner of the De Morgan Association was again the Jeremy Bentham Room at UCL. Over the years it has been known by other names – most of us will remember it as the Upper Hall, one of the refectories. Its relatively new name was particularly fitting since our Guest of Honour was Dr Andew Murrison MP, who spoke on some of the work of Jeremy Bentham as a social reformer. Dr Murrison is currently Shadow Minister of Defence, having previously been Shadow Minister of Health. His political career mirrors his earlier career in the medical branch of the Royal Navy, when research into neurological decompression illness led to the award of an MD and the Gilbert Blane Medal. This year marked the 10th Anniversary of the death of Sir James Lighthill on 17 July 1998. Sir James was one of Britain’s great mathematicians and a former Provost of UCL and, on his retirement, a member of the Department of Mathematics. He died tragically while engaging in one of his hobbies of long distance swimming. In this issue of the Newsletter, Professor Julian Hunt, who was the founding Dr Andrew Murrison speaking at the Director of the Lighthill Institute of Mathematical Sciences, De Morgan Association Dinner assesses Lighthill’s legacy to the mathematical sciences some 10 years after his untimely death. The year also marked the retirement of two distinguished members of the Department – Professor John Jayne and Dr Kalvis Jansons – and the arrival of one new member of the academic staff, Professor Alexey Zaikin.
    [Show full text]
  • Raising the Bar Sydney 2018 Warwick Holmes – to Infinity and Beyond
    Raising the Bar Sydney 2018 Warwick Holmes – To infinity and beyond Welcome to the podcast series of "Raising the Bar Sydney." Raising the bar in 2018 saw 20 University of Sydney academics take their research out of the lecture theatre and into bars across Sydney, all on one night. In this podcast, you'll hear Warrick Holmes' talk, "To Infinity and beyond." Enjoy the talk. [ Applause ] Okay, ladies and gentlemen, thank you very much indeed for coming this evening to the University of Sydney's "Raising The Bar." The theme of my talk tonight is titled, and I've just forgotten what it is, "To Infinity and Beyond." That's right. Okay. So, tonight I'm going to be presenting to you some themes about space engineering and space science. And the relevance to Australia. And I'm going tp put this in the format of giving you some antidotes about space engineering and some of the history of engineering in Australia. Before I start, I just want to check that you've all got the right drinks, because this a bar. I understand there's some interesting space cocktails here tonight. So, I tonight have a Bailey's Comet with me, you see, Bailey's Comet. There's Pink Galactic Garbo Blasters I believe courtesy of Douglas Adams. And did you know that there was a crater on the moon called beer crater, which I just feel is appropriate somehow for tonight. So, because we're in a bar, I think the general theme I have, I'm going to ask you some questions first of all and then half an hour later you're going to ask me questions, okay.
    [Show full text]
  • 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.
    [Show full text]
  • Golden Yearbook
    Golden Yearbook Golden Yearbook Stories from graduates of the 1930s to the 1960s Foreword from the Vice-Chancellor and Principal ���������������������������������������������������������5 Message from the Chancellor ��������������������������������7 — Timeline of significant events at the University of Sydney �������������������������������������8 — The 1930s The Great Depression ������������������������������������������ 13 Graduates of the 1930s ���������������������������������������� 14 — The 1940s Australia at war ��������������������������������������������������� 21 Graduates of the 1940s ����������������������������������������22 — The 1950s Populate or perish ���������������������������������������������� 47 Graduates of the 1950s ����������������������������������������48 — The 1960s Activism and protest ������������������������������������������155 Graduates of the 1960s ���������������������������������������156 — What will tomorrow bring? ��������������������������������� 247 The University of Sydney today ���������������������������248 — Index ����������������������������������������������������������������250 Glossary ����������������������������������������������������������� 252 Produced by Marketing and Communications, the University of Sydney, December 2016. Disclaimer: The content of this publication includes edited versions of original contributions by University of Sydney alumni and relevant associated content produced by the University. The views and opinions expressed are those of the alumni contributors and do
    [Show full text]
  • 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.
    [Show full text]