Saunders Mac Lane, the Knight of Mathematics S. S
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Mathematics People
Mathematics People symmetric spaces, L²-cohomology, arithmetic groups, and MacPherson Awarded Hopf the Langlands program. The list is by far not complete, and Prize we try only to give a representative selection of his contri- bution to mathematics. He influenced a whole generation Robert MacPherson of the Institute for Advanced Study of mathematicians by giving them new tools to attack has been chosen the first winner of the Heinz Hopf Prize difficult problems and teaching them novel geometric, given by ETH Zurich for outstanding scientific work in the topological, and algebraic ways of thinking.” field of pure mathematics. MacPherson, a leading expert Robert MacPherson was born in 1944 in Lakewood, in singularities, delivered the Heinz Hopf Lectures, titled Ohio. He received his B.A. from Swarthmore College in “How Nature Tiles Space”, in October 2009. The prize also 1966 and his Ph.D. from Harvard University in 1970. He carries a cash award of 30,000 Swiss francs, approximately taught at Brown University from 1970 to 1987 and at equal to US$30,000. the Massachusetts Institute of Technology from 1987 to The following quotation was taken from a tribute to 1994. He has been at the Institute for Advanced Study in MacPherson by Gisbert Wüstholz of ETH Zurich: “Singu- Princeton since 1994. His work has introduced radically larities can be studied in different ways using analysis, new approaches to the topology of singular spaces and or you can regard them as geometric phenomena. For the promoted investigations across a great spectrum of math- latter, their study demands a deep geometric intuition ematics. -
LINEAR ALGEBRA METHODS in COMBINATORICS László Babai
LINEAR ALGEBRA METHODS IN COMBINATORICS L´aszl´oBabai and P´eterFrankl Version 2.1∗ March 2020 ||||| ∗ Slight update of Version 2, 1992. ||||||||||||||||||||||| 1 c L´aszl´oBabai and P´eterFrankl. 1988, 1992, 2020. Preface Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent decades. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint at the plausibility of some link between the two areas. A more profound connection, the use of determinants in combinatorial enumeration goes back at least to the work of Kirchhoff in the middle of the 19th century on counting spanning trees in an electrical network. It is much less known, however, that quite apart from the theory of determinants, the elements of the theory of linear spaces has found striking applications to the theory of families of finite sets. With a mere knowledge of the concept of linear independence, unexpected connections can be made between algebra and combinatorics, thus greatly enhancing the impact of each subject on the student's perception of beauty and sense of coherence in mathematics. If these adjectives seem inflated, the reader is kindly invited to open the first chapter of the book, read the first page to the point where the first result is stated (\No more than 32 clubs can be formed in Oddtown"), and try to prove it before reading on. (The effect would, of course, be magnified if the title of this volume did not give away where to look for clues.) What we have said so far may suggest that the best place to present this material is a mathematics enhancement program for motivated high school students. -
Publications of Members, 1930-1954
THE INSTITUTE FOR ADVANCED STUDY PUBLICATIONS OF MEMBERS 1930 • 1954 PRINCETON, NEW JERSEY . 1955 COPYRIGHT 1955, BY THE INSTITUTE FOR ADVANCED STUDY MANUFACTURED IN THE UNITED STATES OF AMERICA BY PRINCETON UNIVERSITY PRESS, PRINCETON, N.J. CONTENTS FOREWORD 3 BIBLIOGRAPHY 9 DIRECTORY OF INSTITUTE MEMBERS, 1930-1954 205 MEMBERS WITH APPOINTMENTS OF LONG TERM 265 TRUSTEES 269 buH FOREWORD FOREWORD Publication of this bibliography marks the 25th Anniversary of the foundation of the Institute for Advanced Study. The certificate of incorporation of the Institute was signed on the 20th day of May, 1930. The first academic appointments, naming Albert Einstein and Oswald Veblen as Professors at the Institute, were approved two and one- half years later, in initiation of academic work. The Institute for Advanced Study is devoted to the encouragement, support and patronage of learning—of science, in the old, broad, undifferentiated sense of the word. The Institute partakes of the character both of a university and of a research institute j but it also differs in significant ways from both. It is unlike a university, for instance, in its small size—its academic membership at any one time numbers only a little over a hundred. It is unlike a university in that it has no formal curriculum, no scheduled courses of instruction, no commitment that all branches of learning be rep- resented in its faculty and members. It is unlike a research institute in that its purposes are broader, that it supports many separate fields of study, that, with one exception, it maintains no laboratories; and above all in that it welcomes temporary members, whose intellectual development and growth are one of its principal purposes. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
Perspective the PNAS Way Back Then
Proc. Natl. Acad. Sci. USA Vol. 94, pp. 5983–5985, June 1997 Perspective The PNAS way back then Saunders Mac Lane, Chairman Proceedings Editorial Board, 1960–1968 Department of Mathematics, University of Chicago, Chicago, IL 60637 Contributed by Saunders Mac Lane, March 27, 1997 This essay is to describe my experience with the Proceedings of ings. Bronk knew that the Proceedings then carried lots of math. the National Academy of Sciences up until 1970. Mathemati- The Council met. Detlev was not a man to put off till to cians and other scientists who were National Academy of tomorrow what might be done today. So he looked about the Science (NAS) members encouraged younger colleagues by table in that splendid Board Room, spotted the only mathe- communicating their research announcements to the Proceed- matician there, and proposed to the Council that I be made ings. For example, I can perhaps cite my own experiences. S. Chairman of the Editorial Board. Then and now the Council Eilenberg and I benefited as follows (communicated, I think, did not often disagree with the President. Probably nobody by M. H. Stone): ‘‘Natural isomorphisms in group theory’’ then knew that I had been on the editorial board of the (1942) Proc. Natl. Acad. Sci. USA 28, 537–543; and “Relations Transactions, then the flagship journal of the American Math- between homology and homotopy groups” (1943) Proc. Natl. ematical Society. Acad. Sci. USA 29, 155–158. Soon after this, the Treasurer of the Academy, concerned The second of these papers was the first introduction of a about costs, requested the introduction of page charges for geometrical object topologists now call an “Eilenberg–Mac papers published in the Proceedings. -
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. -
Humanizing Mathematics and Its Philosophy a Review by Joseph Auslander
BOOK REVIEW Humanizing Mathematics and its Philosophy A Review by Joseph Auslander Communicated by Cesar E. Silva Humanizing Mathematics and its Philosophy: he wrote and coauthored with Philip Davis and Vera John- Essays Celebrating the 90th Birthday of Reuben Hersh Steiner several books and developed what he terms a Bharath Sriraman, editor Humanist philosophy of mathematics. He has also been a Birkhäuser, 2017 frequent book reviewer for Notices.1 Hardcover, 363 pages ISBN: 978-3-319-61230-0 Although he was not trained as a philosopher, Reuben Hersh has emerged as a major figure in the philosophy of mathematics. His Humanist view is probably the most cogent expression contrasting the dominant philosophies of Platonism and Formalism. Hersh has had a remarkable career. He was born in the Bronx, to immigrant working class parents. He graduated from Harvard at age nineteen with a major in English and worked for some time as a journalist, followed by a period of working as a machinist. He then attended the Courant Institute from which he obtained a PhD in 1962, under the supervision of Peter Lax. Hersh settled into a conventional academic career as a professor at The University of New Mexico, pursuing research mostly in partial differential equations. But beginning in the 1970s he wrote a number of expository articles, in Scientific American, Mathematical Reuben Hersh with co-author Vera John-Steiner Intelligencer, and Advances in Mathematics. Subsequently, signing copies of their book Loving and Hating Mathematics: Challenging the Myths of Mathematical Life Joseph Auslander is Professor Emeritus of Mathematics at the at the Princeton University Press Exhibit, JMM 2011. -
Remembering Paul Cohen (1934–2007) Peter Sarnak, Coordinating Editor
Remembering Paul Cohen (1934–2007) Peter Sarnak, Coordinating Editor Paul Joseph Cohen, one of the stars some classic texts. There he got his first exposure of twentieth-century mathematics, to modern mathematics, and it molded him as a passed away in March 2007 at the mathematician. He tried working with André Weil age of seventy-two. Blessed with a in number theory, but that didn’t pan out, and unique mathematical gift for solving instead he studied with Antoni Zygmund, writing difficult and central problems, he a thesis in Fourier series on the topic of sets of made fundamental breakthroughs uniqueness. In Chicago he formed many long- in a number of fields, the most spec- lasting friendships with some of his fellow stu- tacular being his resolution of Hil- dents (for example, John Thompson, who re- bert’s first problem—the continuum mained a lifelong close friend). hypothesis. The period after he graduated with a Ph.D. Like many of the mathematical gi- was very productive, and he enjoyed a series of Paul Cohen ants of the past, Paul did not restrict successes in his research. He solved a problem his attention to any one specialty. of Walter Rudin in group algebras, and soon To him mathematics was a unified subject that after that he obtained his first breakthrough on one could master broadly. He had a deep under- what was considered to be a very difficult prob- standing of most areas, and he taught advanced lem—the Littlewood conjecture. He gave the first courses in logic, analysis, differential equations, nontrivial lower bound for the L1 norm of trigo- algebra, topology, Lie theory, and number theory nometric polynomials on the circle whose Fourier on a regular basis. -
Differential Geometry in the Large Seminar Lectures New York University 1946 and Stanford University 1956 Series: Lecture Notes in Mathematics
springer.com Heinz Hopf Differential Geometry in the Large Seminar Lectures New York University 1946 and Stanford University 1956 Series: Lecture Notes in Mathematics These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J. W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential 2nd ed. 1989, VIII, 192 p. Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Printed book Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of Softcover gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, . 29,95 € | £26.99 | $49.95 [1]32,05 € (D) | 32,95 € (A) | CHF 43,04 eBook 24,60 € | £20.99 | $34.99 [2]24,60 € (D) | 24,60 € (A) | CHF 34,00 Available from your library or springer.com/shop MyCopy [3] Printed eBook for just € | $ 24.99 springer.com/mycopy Error[en_EN | Export.Bookseller. -
Council Congratulates Exxon Education Foundation
from.qxp 4/27/98 3:17 PM Page 1315 From the AMS ics. The Exxon Education Foundation funds programs in mathematics education, elementary and secondary school improvement, undergraduate general education, and un- dergraduate developmental education. —Timothy Goggins, AMS Development Officer AMS Task Force Receives Two Grants The AMS recently received two new grants in support of its Task Force on Excellence in Mathematical Scholarship. The Task Force is carrying out a program of focus groups, site visits, and information gathering aimed at developing (left to right) Edward Ahnert, president of the Exxon ways for mathematical sciences departments in doctoral Education Foundation, AMS President Cathleen institutions to work more effectively. With an initial grant Morawetz, and Robert Witte, senior program officer for of $50,000 from the Exxon Education Foundation, the Task Exxon. Force began its work by organizing a number of focus groups. The AMS has now received a second grant of Council Congratulates Exxon $50,000 from the Exxon Education Foundation, as well as a grant of $165,000 from the National Science Foundation. Education Foundation For further information about the work of the Task Force, see “Building Excellence in Doctoral Mathematics De- At the Summer Mathfest in Burlington in August, the AMS partments”, Notices, November/December 1995, pages Council passed a resolution congratulating the Exxon Ed- 1170–1171. ucation Foundation on its fortieth anniversary. AMS Pres- ident Cathleen Morawetz presented the resolution during —Timothy Goggins, AMS Development Officer the awards banquet to Edward Ahnert, president of the Exxon Education Foundation, and to Robert Witte, senior program officer with Exxon. -
“All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematical Society
Journal of Humanistic Mathematics Volume 10 | Issue 2 July 2020 “All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematical Society Michael J. Barany University of Edinburgh Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the History of Science, Technology, and Medicine Commons, Mathematics Commons, and the United States History Commons Recommended Citation Barany, M. J. "“All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematical Society," Journal of Humanistic Mathematics, Volume 10 Issue 2 (July 2020), pages 527-538. DOI: 10.5642/jhummath.202002.24 . Available at: https://scholarship.claremont.edu/jhm/ vol10/iss2/24 ©2020 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. “All of These Political Questions”: Anticommunism, Racism, and the Origin of the Notices of the American Mathematical Society Cover Page Footnote This essay began as an extended thread on Twitter, and I would like to thank my Twitter interlocutors from the mathematics community for challenging and encouraging me to address my historical research to current debates in the discipline. -
Prepared to Meet You Where You Are Annual Report 2019 Annual Message We Are Delighted to Present Our 2019 Annual Report
Prepared to Meet You Where You Are Annual Report 2019 Annual Message We are delighted to present our 2019 Annual Report. We must be prepared to meet people where they Finally, our heartfelt thanks go out to our entire Board, Every year, as we “look back,” we are amazed at how are and we’re doing just that. Our short list includes our volunteers and our 500-plus staff members— much CJE offers to the community. It is often hard a focus on the emerging field of digital health and social workers, nurses, care managers, bus drivers, to choose which programs and services to highlight. assistive technology, the highly-anticipated opening cooks, resident care assistants, therapists and a Very few organizations nationwide offer the breadth of of Tamarisk NorthShore, the thoughtful elevation of whole host of hardworking individuals—who provide programs and services that we do to enhance the lives educational programming for the Sandwich Generation services to more than 20,000 older adults and their of older adults in the Jewish and larger community. and the expansion of supportive services to seniors family members each year. With your continued who want to stay in their own homes safely and with support, we can keep moving forward with creativity In this report, we illustrate how CJE’s Continuum dignity. and intention to “meet people” wherever they are on of Care stands without walls—prepared to “meet” CJE’s Continuum of Care. people wherever they might be in life, utilizing any As we move closer to our 50-year milestone, CJE has of our 35-plus programs to address their individual a strong foundation on which to build for the future.