Mathematical Apocrypha Redux Originally Published by the Mathematical Association of America, 2005
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Hilbert Constance Reid
Hilbert Constance Reid Hilbert c COPERNICUS AN IMPRINT OF SPRINGER-VERLAG © 1996 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc in 1996 All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library ofCongress Cataloging·in-Publication Data Reid, Constance. Hilbert/Constance Reid. p. Ctn. Originally published: Berlin; New York: Springer-Verlag, 1970. Includes bibliographical references and index. ISBN 978-0-387-94674-0 ISBN 978-1-4612-0739-9 (eBook) DOI 10.1007/978-1-4612-0739-9 I. Hilbert, David, 1862-1943. 2. Mathematicians-Germany Biography. 1. Title. QA29.HsR4 1996 SIO'.92-dc20 [B] 96-33753 Manufactured in the United States of America. Printed on acid-free paper. 9 8 7 6 543 2 1 ISBN 978-0-387-94674-0 SPIN 10524543 Questions upon Rereading Hilbert By 1965 I had written several popular books, such as From liro to Infinity and A Long Way from Euclid, in which I had attempted to explain certain easily grasped, although often quite sophisticated, mathematical ideas for readers very much like myself-interested in mathematics but essentially untrained. At this point, with almost no mathematical training and never having done any bio graphical writing, I became determined to write the life of David Hilbert, whom many considered the profoundest mathematician of the early part of the 20th century. Now, thirty years later, rereading Hilbert, certain questions come to my mind. -
These Links No Longer Work. Springer Have Pulled the Free Plug
Sign up for a GitHub account Sign in Instantly share code, notes, and snippets. Create a gist now bishboria / springer-free-maths-books.md Last active 10 minutes ago Code Revisions 7 Stars 2104 Forks 417 Embed <script src="https://gist.githu b .coDmo/wbinslohabodr ZiIaP/8326b17bbd652f34566a.js"></script> Springer made a bunch of books available for free, these were the direct links springer-free-maths-books.md Raw These links no longer work. Springer have pulled the free plug. Graduate texts in mathematics duplicates = multiple editions A Classical Introduction to Modern Number Theory, Kenneth Ireland Michael Rosen A Classical Introduction to Modern Number Theory, Kenneth Ireland Michael Rosen A Course in Arithmetic, Jean-Pierre Serre A Course in Computational Algebraic Number Theory, Henri Cohen A Course in Differential Geometry, Wilhelm Klingenberg A Course in Functional Analysis, John B. Conway A Course in Homological Algebra, P. J. Hilton U. Stammbach A Course in Homological Algebra, Peter J. Hilton Urs Stammbach A Course in Mathematical Logic, Yu. I. Manin A Course in Number Theory and Cryptography, Neal Koblitz A Course in Number Theory and Cryptography, Neal Koblitz A Course in Simple-Homotopy Theory, Marshall M. Cohen A Course in p-adic Analysis, Alain M. Robert A Course in the Theory of Groups, Derek J. S. Robinson A Course in the Theory of Groups, Derek J. S. Robinson A Course on Borel Sets, S. M. Srivastava A Course on Borel Sets, S. M. Srivastava A First Course in Noncommutative Rings, T. Y. Lam A First Course in Noncommutative Rings, T. Y. Lam A Hilbert Space Problem Book, P. -
Mathematician Awarded Nobel Prize Growing Optimism That Fermat's
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Mathematician Awarded Nobel Prize Volume 14, Number 6 Keith Devlin The awarding of the Nobel Prize in econom It was the application ics to the American John Nash on October of Nash's work in eco II th meant that for the firsttime in the 93-year nomic theory that led to history of the Nobel Prizes, the prize was his recent Nobel Prize, In this Issue awarded for work in pure mathematics. which he shares with fellow American John When the Swedish chemist, engineer, and phi Harsanyi and German 3 MAA Secretary's lanthropistAlfred Bernhard Nobel established Reinhard Selten. Report the awards in 1901, he stipulated chemistry, Nash's contribution to physics, physiology and medicine, and litera the combined work ture, but did not create a prize for mathematics. 4 Joint Mathematics which won the award It has been rumored that a particularly bad was in game theory. Meetings Update experience in mathematics at high school led to this exclusion of the "queen of sciences", or Nash's key idea-known nowadays as Nash 6 Search Committee it may simply be that Nobel felt that math equilibrium-was developed in his Ph.D. the Diary ematics was not, in itself, of sufficient sis submitted to the Princeton University relevance to human development to warrant Mathematics Department in 1950, when Nash its own award. Whateverthe reason, the math was just 22 years old. The thesis had taken him 10 Networks in ematicians have had to make do with their a mere two years to complete. -
Constance Reid
Constance Reid John Ewing, former director of the American Mathematical Society, says this of Constance Reid: “ She has a special talent for understanding mathematicians and their culture. She understands us. She is the Boswell for mathematics – a biographer who has made the mathematical life understandable to the general public and to mathematicians themselves. Her work has enriched our profession.” The “autobiography” of her sister Julia Robinson has been a source of inspiration for many young women contemplating careers in mathematics, and her biography of David Hilbert stands as one of the best mathematical biographies ever written. It is no exaggeration to say that publication of Hilbert made her a star among mathematical biographers. Her five lively and penetrating biographies of mathematicians have been highly praised and constitute a great contribution to the world of mathematics. She has set a high standard for future biographers. We are proud that she was a member of our section. Although the formal mathematical education of Constance Reid concluded with high school algebra and geometry, she was able to understand mathematical ideas well enough to write three best - selling popularizations of mathematics: From Zero to Infinity (1955), Introduction to Higher Mathematics (1959), and A Long Way From Euclid (1963). Several mathematicians have commented on the influence of From Zero to Infinity on their development. Her writing ability was early demonstrated in her book Slacks and Calluses(1944), an account of her working for a summer on a bomber factory assembly line in World War II. At the time she was a high school English teacher in San Diego and only twenty - six. -
Bibliography
Bibliography [AK98] V. I. Arnold and B. A. Khesin, Topological methods in hydrodynamics, Springer- Verlag, New York, 1998. [AL65] Holt Ashley and Marten Landahl, Aerodynamics of wings and bodies, Addison- Wesley, Reading, MA, 1965, Section 2-7. [Alt55] M. Altman, A generalization of Newton's method, Bulletin de l'academie Polonaise des sciences III (1955), no. 4, 189{193, Cl.III. [Arm83] M.A. Armstrong, Basic topology, Springer-Verlag, New York, 1983. [Bat10] H. Bateman, The transformation of the electrodynamical equations, Proc. Lond. Math. Soc., II, vol. 8, 1910, pp. 223{264. [BB69] N. Balabanian and T.A. Bickart, Electrical network theory, John Wiley, New York, 1969. [BLG70] N. N. Balasubramanian, J. W. Lynn, and D. P. Sen Gupta, Differential forms on electromagnetic networks, Butterworths, London, 1970. [Bos81] A. Bossavit, On the numerical analysis of eddy-current problems, Computer Methods in Applied Mechanics and Engineering 27 (1981), 303{318. [Bos82] A. Bossavit, On finite elements for the electricity equation, The Mathematics of Fi- nite Elements and Applications IV (MAFELAP 81) (J.R. Whiteman, ed.), Academic Press, 1982, pp. 85{91. [Bos98] , Computational electromagnetism: Variational formulations, complementar- ity, edge elements, Academic Press, San Diego, 1998. [Bra66] F.H. Branin, The algebraic-topological basis for network analogies and the vector cal- culus, Proc. Symp. Generalised Networks, Microwave Research, Institute Symposium Series, vol. 16, Polytechnic Institute of Brooklyn, April 1966, pp. 453{491. [Bra77] , The network concept as a unifying principle in engineering and physical sciences, Problem Analysis in Science and Engineering (K. Husseyin F.H. Branin Jr., ed.), Academic Press, New York, 1977. -
Women's History Magazine Broadly As Possible
Women’s History Magazine Issue 48, AUTUMN 2004 Issn 1476-6760 Themed Issue: Science, Technology and Education Maria Rentetzi on The Case of the Radium Dial Painters Claire Jones on Grace Chisholm Young in Turn-of-Nineteenth-Century Germany Joyce Goodman on Technical Education, Female Emigration and Nation Building Hull 2004 Conference Report Launch of new WHN Book Prize Clare Evans Prize — Report on 2004 Award and Hypatia Announcement of of Alexandria 2005 Competition c. 370 - 415 Conference 2005 — Mathematician philosopher, Call for Papers teacher and inventor of mechanical devices. th 14 Conference of the Women’s History Network Women, Art and Culture: Historical Perspectives September 2nd- 4th 2005, Southampton Southampton Institute, Sir James Matthews Conference Centre, Southampton, Hants. Papers are welcomed on the following themes: Women and the visual arts; painting, sculpture, architecture, and the decorative arts. Women and the Arts and Crafts Movement/Home Decorating. Women and the performing arts. Women and the literary arts. Women as art objects/images of women. Women as mediators of culture. Women as collectors and benefactors. Plenary Speakers: Frances Borzello on 'Women Artists: Self Portraits' Marina Vaizey on '20th Century Women Collectors' Speakers, papers and a provisional programme will be posted at www.womenshistorynetwork.org as soon as they become available. Papers will be considered for special issues of: Women’s History Magazine & Women’s History Review. Abstracts of 200-300 words should be sent by 30/03/05 to: Dr Anne Anderson, FMAS, Southampton Institute, Southampton, S014 ORF. [email protected] Administrator: Dr. Joyce A. Walker (Women’s History Network) , Department of History, University of Aberdeen, Crombie Annexe, Meston Walk, Old Aberdeen, AB24 3FX E-mail: [email protected] The arrival of this Autumn's Women's History Magazine broadly as possible. -
Constance Reid (1918–2010)
Remembering Constance Reid (1918–2010) Gerald L. Alexanderson Constance Reid will be remembered in mathemat- She was fond of telling at mathematics meet- ics for many years to come. She was not a math- ings of her experience when she approached her ematician, though she had close ties to important publisher with the proposal to write a biography mathematicians, but what she did for mathemat- of the most eminent early-twentieth-century math- ics may have more influence than the research of ematician, David Hilbert. His response was that the many professionals in the field. She would have a only thing that would sell worse than the biography place in history if she had done nothing more than of a mathematician would be a book about South write her biography of David Hilbert. America! But she persisted and found a publisher, Prior to Constance’s ap- Springer. It appeared in 1970 and was an instant pearing on the mathemati- classic, a book for the ages. Beautifully written cal scene, there was rather and carefully researched—she discovered Hilbert’s little to read in mathematics, papers in Göttingen uncatalogued in boxes at the at least in English, beyond Mathematical Institute, thus quite possibly saving textbooks and monographs. them from loss—her book was a sensation and re- Students wishing to learn sulted in many invitations to speak at regional and of the culture of mathemat- national meetings. Her earlier publisher probably ics or amateurs who loved came to regret his quick dismissal of Constance’s mathematics could go to proposal. Times have changed. -
Herbert Busemann (1905--1994)
HERBERT BUSEMANN (1905–1994) A BIOGRAPHY FOR HIS SELECTED WORKS EDITION ATHANASE PAPADOPOULOS Herbert Busemann1 was born in Berlin on May 12, 1905 and he died in Santa Ynez, County of Santa Barbara (California) on February 3, 1994, where he used to live. His first paper was published in 1930, and his last one in 1993. He wrote six books, two of which were translated into Russian in the 1960s. Initially, Busemann was not destined for a mathematical career. His father was a very successful businessman who wanted his son to be- come, like him, a businessman. Thus, the young Herbert, after high school (in Frankfurt and Essen), spent two and a half years in business. Several years later, Busemann recalls that he always wanted to study mathematics and describes this period as “two and a half lost years of my life.” Busemann started university in 1925, at the age of 20. Between the years 1925 and 1930, he studied in Munich (one semester in the aca- demic year 1925/26), Paris (the academic year 1927/28) and G¨ottingen (one semester in 1925/26, and the years 1928/1930). He also made two 1Most of the information about Busemann is extracted from the following sources: (1) An interview with Constance Reid, presumably made on April 22, 1973 and kept at the library of the G¨ottingen University. (2) Other documents held at the G¨ottingen University Library, published in Vol- ume II of the present edition of Busemann’s Selected Works. (3) Busemann’s correspondence with Richard Courant which is kept at the Archives of New York University. -
A Tribute to Dick Askey
A tribute to Dick Askey Tom Koornwinder,∗ Walter Van Asschey and Ole Warnaarz February 2015 (last minor corrections 14 May 2015) Richard A. (Dick) Askey1 was born June 4, 1933 in St. Louis, Missouri. He received his PhD at Princeton University in 1961 under the direction of Salomon Bochner. After instructorships at Washington University and the University of Chicago he joined the faculty of the University of Wisconsin-Madison in 1963, where he became full professor in 1968. Since 2003 he is Professor Emeritus at that same institution. Dick received many awards and distinctions during the course of his mathematical career. He was elected member of the American Academy of Arts and Sciences in 1993 and of the National Academy of Sciences in 1999. Furthermore, he is a Honorary Fellow of the Indian Academy of Sciences and a Fellow of SIAM and of the American Mathematical Society. In 1983 he was an invited speaker at the International Congress of Mathematicians (ICM) in Warszawa. In 2012 he received an hon- orary doctorate from SASTRA University in Kumbakonam, India. Dick Askey's research interests are Special Functions and Orthogonal Polynomials, and more generally Classical Analysis. His works often touch upon aspects of approximation theory, har- monic analysis, number theory, combinatorics and probability theory. He published2 140 research articles in journals, conference proceedings and edited books. His most frequent coauthors are George Gasper, Mourad Ismail and Stephen Wainger. Dick's research publications include two AMS Memoirs: one written with Mourad Ismail in 1984 [7], and one with James Wilson in 1985 [8] on the Askey-Wilson polynomials, probably his most influential publication. -
AN INTEGRAL of PRODUCTS of ULTRASPHERICAL FUNCTIONS and a Q-EXTENSION
AN INTEGRAL OF PRODUCTS OF ULTRASPHERICAL FUNCTIONS AND A q-EXTENSION RICHARD ASKEY, TOM H. KOORNWINDER AND MIZAN RAHMAN ABSTRACT Let Pn(x) and Qn(x) denote the Legendre polynomial of degree n and the usual second solution to the differential equation, respectively. Din showed that J1__ 1 Qn(x) Pm(x) P1(x) dx vanishes when 11-m I < n < l+m, and Askey evaluated the integral for arbitrary integral values of l, m and n. We extend this to the evaluation of J1__ 1 D~(x) Ci,(x) Cf(x) (l -x2) 2•- 1 dx, where C~(x) is the ultraspherical polynomial and D~(x) is the appropriate second solution to the ultraspherical differential equation. A q-extension is found using the continuous q-ultraspherical polynomials of Rogers. Again the integral vanishes when I l-m I < n < l + m. It is shown that this vanishing phenomenon holds for quite general orthogonal polynomials. A related integral of the product of three Bessel functions is also evaluated. 1. Introduction Legendre polynomials Pn are orthogonal polynomials of degree non (-1, I) with constant weight function and with normalization Pn(l) = 1. Corresponding Legendre functions of the second kind Qn are defined on the cut (-1, I) by the principal value integral Qn(X) = ~ L1x11 p ~t; dt, -1 < x < 1, (1.1) cf. [26, (4.9.12) and (4.62.9)]. In a very surprising paper Din [9] showed that [ (x)dx = (l.2) 1 Qn(x)Pm(x)P1 0 when I l-m I< n < l+m. Part of the surprise was the vanishing and part was the fact that such an attractive result did not seem to have been found before. -
Introduction to Representation Theory
STUDENT MATHEMATICAL LIBRARY Volume 59 Introduction to Representation Theory Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, Elena Yudovina with historical interludes by Slava Gerovitch http://dx.doi.org/10.1090/stml/059 STUDENT MATHEMATICAL LIBRARY Volume 59 Introduction to Representation Theory Pavel Etingof Oleg Golberg Sebastian Hensel Tiankai Liu Alex Schwendner Dmitry Vaintrob Elena Yudovina with historical interludes by Slava Gerovitch American Mathematical Society Providence, Rhode Island Editorial Board Gerald B. Folland Brad G. Osgood (Chair) Robin Forman John Stillwell 2010 Mathematics Subject Classification. Primary 16Gxx, 20Gxx. For additional information and updates on this book, visit www.ams.org/bookpages/stml-59 Library of Congress Cataloging-in-Publication Data Introduction to representation theory / Pavel Etingof ...[et al.] ; with historical interludes by Slava Gerovitch. p. cm. — (Student mathematical library ; v. 59) Includes bibliographical references and index. ISBN 978-0-8218-5351-1 (alk. paper) 1. Representations of algebras. 2. Representations of groups. I. Etingof, P. I. (Pavel I.), 1969– QA155.I586 2011 512.46—dc22 2011004787 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. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904- 2294 USA. -
From Abraham De Moivre to Johann Carl Friedrich Gauss
International Journal of Engineering Science Invention (IJESI) ISSN (Online): 2319 – 6734, ISSN (Print): 2319 – 6726 www.ijesi.org ||Volume 7 Issue 6 Ver V || June 2018 || PP 28-34 A Brief Historical Overview Of the Gaussian Curve: From Abraham De Moivre to Johann Carl Friedrich Gauss Edel Alexandre Silva Pontes1 1Department of Mathematics, Federal Institute of Alagoas, Brazil Abstract : If there were only one law of probability to be known, this would be the Gaussian distribution. Faced with this uneasiness, this article intends to discuss about this distribution associated with its graph called the Gaussian curve. Due to the scarcity of texts in the area and the great demand of students and researchers for more information about this distribution, this article aimed to present a material on the history of the Gaussian curve and its relations. In the eighteenth and nineteenth centuries, there were several mathematicians who developed research on the curve, including Abraham de Moivre, Pierre Simon Laplace, Adrien-Marie Legendre, Francis Galton and Johann Carl Friedrich Gauss. Some researchers refer to the Gaussian curve as the "curve of nature itself" because of its versatility and inherent nature in almost everything we find. Virtually all probability distributions were somehow part or originated from the Gaussian distribution. We believe that the work described, the study of the Gaussian curve, its history and applications, is a valuable contribution to the students and researchers of the different areas of science, due to the lack of more detailed research on the subject. Keywords - History of Mathematics, Distribution of Probabilities, Gaussian Curve. ----------------------------------------------------------------------------------------------------------------------------- --------- Date of Submission: 09-06-2018 Date of acceptance: 25-06-2018 ----------------------------------------------------------------------------------------------------------------------------- ---------- I.