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A MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered. -
MY UNFORGETTABLE EARLY YEARS at the INSTITUTE Enstitüde Unutulmaz Erken Yıllarım
MY UNFORGETTABLE EARLY YEARS AT THE INSTITUTE Enstitüde Unutulmaz Erken Yıllarım Dinakar Ramakrishnan `And what was it like,’ I asked him, `meeting Eliot?’ `When he looked at you,’ he said, `it was like standing on a quay, watching the prow of the Queen Mary come towards you, very slowly.’ – from `Stern’ by Seamus Heaney in memory of Ted Hughes, about the time he met T.S.Eliot It was a fortunate stroke of serendipity for me to have been at the Institute for Advanced Study in Princeton, twice during the nineteen eighties, first as a Post-doctoral member in 1982-83, and later as a Sloan Fellow in the Fall of 1986. I had the privilege of getting to know Robert Langlands at that time, and, needless to say, he has had a larger than life influence on me. It wasn’t like two ships passing in the night, but more like a rowboat feeling the waves of an oncoming ship. Langlands and I did not have many conversations, but each time we did, he would make a Zen like remark which took me a long time, at times months (or even years), to comprehend. Once or twice it even looked like he was commenting not on the question I posed, but on a tangential one; however, after much reflection, it became apparent that what he had said had an interesting bearing on what I had been wondering about, and it always provided a new take, at least to me, on the matter. Most importantly, to a beginner in the field like I was then, he was generous to a fault, always willing, whenever asked, to explain the subtle aspects of his own work. -
Sir Andrew J. Wiles
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM. -
Robert P. Langlands Receives the Abel Prize
Robert P. Langlands receives the Abel Prize The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2018 to Robert P. Langlands of the Institute for Advanced Study, Princeton, USA “for his visionary program connecting representation theory to number theory.” Robert P. Langlands has been awarded the Abel Prize project in modern mathematics has as wide a scope, has for his work dating back to January 1967. He was then produced so many deep results, and has so many people a 30-year-old associate professor at Princeton, working working on it. Its depth and breadth have grown and during the Christmas break. He wrote a 17-page letter the Langlands program is now frequently described as a to the great French mathematician André Weil, aged 60, grand unified theory of mathematics. outlining some of his new mathematical insights. The President of the Norwegian Academy of Science and “If you are willing to read it as pure speculation I would Letters, Ole M. Sejersted, announced the winner of the appreciate that,” he wrote. “If not – I am sure you have a 2018 Abel Prize at the Academy in Oslo today, 20 March. waste basket handy.” Biography Fortunately, the letter did not end up in a waste basket. His letter introduced a theory that created a completely Robert P. Langlands was born in New Westminster, new way of thinking about mathematics: it suggested British Columbia, in 1936. He graduated from the deep links between two areas, number theory and University of British Columbia with an undergraduate harmonic analysis, which had previously been considered degree in 1957 and an MSc in 1958, and from Yale as unrelated. -
Commodity and Energy Markets Conference at Oxford University
Commodity and Energy Markets Conference Annual Meeting 2017 th th 14 - 15 June Page | 1 Commodity and Energy Markets Conference Contents Welcome 3 Essential Information 4 Bird’s-eye view of programme 6 Detailed programme 8 Venue maps 26 Mezzanine level of Andrew Wiles Building 27 Local Information 28 List of Participants 29 Keynote Speakers 33 Academic journals: special issues 34 Sponsors 35 Page | 2 Welcome On behalf of the Mathematical Institute, it is our great pleasure to welcome you to the University of Oxford for the Commodity and Energy Markets annual conference (2017). The Commodity and Energy Markets annual conference 2017 is the latest in a long standing series of meetings. Our first workshop was held in London in 2004, and after that we expanded the scope and held yearly conferences in different locations across Europe. Nowadays, the Commodity and Energy Markets conference is the benchmark meeting for academics who work in this area. This year’s event covers a wide range of topics in commodities and energy. We highlight three keynote talks. Prof Hendrik Bessembinder (Arizona State University) will talk on “Measuring returns to those who invest in energy through futures”, and Prof Sebastian Jaimungal (University of Toronto) will talk about “Stochastic Control in Commodity & Energy Markets: Model Uncertainty, Algorithmic Trading, and Future Directions”. Moreover, Tony Cocker, E.ON’s Chief Executive Officer, will share his views and insights into the role of mathematical modelling in the energy industry. In addition to the over 100 talks, a panel of academics and professional experts will discuss “The future of energy trading in the UK and Europe: a single energy market?” The roundtable is sponsored by the Italian Association of Energy Suppliers and Traders (AIGET) and European Energy Retailers (EER). -
Math Spans All Dimensions
March 2000 THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA Math Spans All Dimensions April 2000 is Math Awareness Month Interactive version of the complete poster is available at: http://mam2000.mathforum.com/ FOCUS March 2000 FOCUS is published by the Mathematical Association of America in January. February. March. April. May/June. August/September. FOCUS October. November. and December. a Editor: Fernando Gouvea. Colby College; March 2000 [email protected] Managing Editor: Carol Baxter. MAA Volume 20. Number 3 [email protected] Senior Writer: Harry Waldman. MAA In This Issue [email protected] Please address advertising inquiries to: 3 "Math Spans All Dimensions" During April Math Awareness Carol Baxter. MAA; [email protected] Month President: Thomas Banchoff. Brown University 3 Felix Browder Named Recipient of National Medal of Science First Vice-President: Barbara Osofsky. By Don Albers Second Vice-President: Frank Morgan. Secretary: Martha Siegel. Treasurer: Gerald 4 Updating the NCTM Standards J. Porter By Kenneth A. Ross Executive Director: Tina Straley 5 A Different Pencil Associate Executive Director and Direc Moving Our Focus from Teachers to Students tor of Publications and Electronic Services: Donald J. Albers By Ed Dubinsky FOCUS Editorial Board: Gerald 6 Mathematics Across the Curriculum at Dartmouth Alexanderson; Donna Beers; J. Kevin By Dorothy I. Wallace Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Maeve McCarthy; Peter Renz; Annie 7 ARUME is the First SIGMAA Selden; Jon Scott; Ravi Vakil. Letters to the editor should be addressed to 8 Read This! Fernando Gouvea. Colby College. Dept. of Mathematics. Waterville. ME 04901. 8 Raoul Bott and Jean-Pierre Serre Share the Wolf Prize Subscription and membership questions 10 Call For Papers should be directed to the MAA Customer Thirteenth Annual MAA Undergraduate Student Paper Sessions Service Center. -
Andrew Wiles and Fermat's Last Theorem
Andrew Wiles and Fermat's Last Theorem Ton Yeh A great figure in modern mathematics Sir Andrew Wiles is renowned throughout the world for having cracked the problem first posed by Fermat in 1637: the non-existence of positive integer solutions to an + bn = cn for n ≥ 3. Wiles' famous journey towards his proof { the surprising connection with elliptic curves, the apparent success, the discovery of an error, the despondency, and then the flash of inspiration which saved the day { is known to layman and professional mathematician alike. Therefore, the fact that Sir Andrew spent his undergraduate years at Merton College is a great honour for us. In this article we discuss simple number-theoretic ideas relating to Fermat's Last Theorem, which may be of interest to current or prospective students, or indeed to members of the public. Easier aspects of Fermat's Last Theorem It goes without saying that the non-expert will have a tough time getting to grips with Andrew Wiles' proof. What follows, therefore, is a sketch of much simpler and indeed more classical ideas related to Fermat's Last Theorem. As a regrettable consequence, things like algebraic topology, elliptic curves, modular functions and so on have to be omitted. As compensation, the student or keen amateur will gain accessible insight from this section; he will also appreciate the shortcomings of these classical approaches and be motivated to prepare himself for more advanced perspectives. Our aim is to determine what can be said about the solutions to an + bn = cn for positive integers a; b; c. -
View This Volume's Front and Back Matter
Expansion in Finite Simple Groups of Lie Type Terence Tao Graduate Studies in Mathematics Volume 164 American Mathematical Society Expansion in Finite Simple Groups of Lie Type https://doi.org/10.1090//gsm/164 Expansion in Finite Simple Groups of Lie Type Terence Tao Graduate Studies in Mathematics Volume 164 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Dan Abramovich Daniel S. Freed Rafe Mazzeo (Chair) Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 05C81, 11B30, 20C33, 20D06, 20G40. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-164 Library of Congress Cataloging-in-Publication Data Tao, Terence, 1975 Expansion in finite simple groups of Lie type / Terence Tao. pages cm. – (Graduate studies in mathematics ; volume 164) Includes bibliographical references and index. ISBN 978-1-4704-2196-0 (alk. paper) 1. Finite simple groups. 2. Lie groups. I. Title. QA387.T356 2015 512.482–dc23 2014049154 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 select pages 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. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. For more information, please visit: http://www.ams.org/rightslink. Send requests for translation rights and licensed reprints to [email protected]. -
Linking Together Members of the Mathematical Carlos Rocha, University of Lisbon; Jean Taylor, Cour- Community from the US and Abroad
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features Epimorphism Theorem Prime Numbers Interview J.-P. Bourguignon Societies European Physical Society Research Centres ESI Vienna December 2013 Issue 90 ISSN 1027-488X S E European M M Mathematical E S Society Cover photo: Jean-François Dars Mathematics and Computer Science from EDP Sciences www.esaim-cocv.org www.mmnp-journal.org www.rairo-ro.org www.esaim-m2an.org www.esaim-ps.org www.rairo-ita.org Contents Editorial Team European Editor-in-Chief Ulf Persson Matematiska Vetenskaper Lucia Di Vizio Chalmers tekniska högskola Université de Versailles- S-412 96 Göteborg, Sweden St Quentin e-mail: [email protected] Mathematical Laboratoire de Mathématiques 45 avenue des États-Unis Zdzisław Pogoda 78035 Versailles cedex, France Institute of Mathematicsr e-mail: [email protected] Jagiellonian University Society ul. prof. Stanisława Copy Editor Łojasiewicza 30-348 Kraków, Poland Chris Nunn e-mail: [email protected] Newsletter No. 90, December 2013 119 St Michaels Road, Aldershot, GU12 4JW, UK Themistocles M. Rassias Editorial: Meetings of Presidents – S. Huggett ............................ 3 e-mail: [email protected] (Problem Corner) Department of Mathematics A New Cover for the Newsletter – The Editorial Board ................. 5 Editors National Technical University Jean-Pierre Bourguignon: New President of the ERC .................. 8 of Athens, Zografou Campus Mariolina Bartolini Bussi GR-15780 Athens, Greece Peter Scholze to Receive 2013 Sastra Ramanujan Prize – K. Alladi 9 (Math. Education) e-mail: [email protected] DESU – Universitá di Modena e European Level Organisations for Women Mathematicians – Reggio Emilia Volker R. Remmert C. Series ............................................................................... 11 Via Allegri, 9 (History of Mathematics) Forty Years of the Epimorphism Theorem – I-42121 Reggio Emilia, Italy IZWT, Wuppertal University [email protected] D-42119 Wuppertal, Germany P. -
Andrew Neitzke
Address: Department of Mathematics Andrew Neitzke University of Texas at Austin 1 University Station, C1200 Curriculum Vitae Austin, TX 78712, USA Email: [email protected] October 2019 WWW: www.ma.utexas.edu/users/neitzke PGP key at: www.ma.utexas.edu/users/neitzke/pubkey.asc Education 2005 Harvard University: Ph.D. in Physics. Advisor: Cumrun Vafa. 1999 Cambridge University: Certificate of Advanced Study in Mathematics. 1998 Princeton University: AB Degree in Mathematics. Employment 2015{present University of Texas at Austin, Department of Mathematics: Associate professor. 2009{2015 University of Texas at Austin, Department of Mathematics: Assistant professor. 2008{2009 Harvard University, Department of Physics: Postdoctoral researcher. 2005{2008 Institute for Advanced Study, Princeton, School of Natural Sciences: Member. Awards and grants 2018 Fellow of the American Mathematical Society (2019 class). 2017 National Science Foundation grant 1711692 (DMS). 2016 Simons Fellowship in Mathematics. 2012 National Science Foundation CAREER grant 1151693 (DMS). 2012 Co-PI on National Science Foundation FRG grant 1160461 (DMS). 2012 John R. Durbin Teaching Excellence Award in Mathematics, UT Austin. 2010 National Science Foundation grant 1006046 (DMS). 2000 NDSEG Graduate Fellowship. 1998 British Marshall Scholarship. 1998 Valedictorian, Princeton University, Class of 1998. External talks since 2011 Multi-lecture series are listed in bold. 2019 MSRI, Berkeley: Four lectures. 2019 Park City Mathematics Institute: Four lectures. 2019 Boston University (math seminar). 2018 Perimeter (Higher Algebra in Mathematical Physics). 2018 Sendai (String-Math 2018). 2018 BIRS, Oaxaca (Higgs Bundles and Harmonic Maps of Riemann Surfaces). 2018 CIRM, Marseilles (Vector Bundles over Algebraic Curves). 2018 Michigan State University (Cluster Algebras and Mathematical Physics). -
Andrew Neitzke
Address: Department of Mathematics Andrew Neitzke University of Texas at Austin 1 University Station, C1200 Curriculum Vitae Austin, TX 78712, USA Email: [email protected] January 2019 WWW: www.ma.utexas.edu/users/neitzke PGP key at: www.ma.utexas.edu/users/neitzke/pubkey.asc Education 2005 Harvard University: Ph.D. in Physics. Advisor: Cumrun Vafa. 1999 Cambridge University: Certificate of Advanced Study in Mathematics. 1998 Princeton University: AB Degree in Mathematics. Employment 2015{present University of Texas at Austin, Department of Mathematics: Associate professor. 2009{2015 University of Texas at Austin, Department of Mathematics: Assistant professor. 2008{2009 Harvard University, Department of Physics: Postdoctoral researcher. 2005{2008 Institute for Advanced Study, Princeton, School of Natural Sciences: Member. Awards and grants 2018 Fellow of the American Mathematical Society (2019 class). 2017 National Science Foundation grant 1711692 (DMS). 2016 Simons Fellowship in Mathematics. 2012 National Science Foundation CAREER grant 1151693 (DMS). 2012 Co-PI on National Science Foundation FRG grant 1160461 (DMS). 2012 John R. Durbin Teaching Excellence Award in Mathematics, UT Austin. 2010 National Science Foundation grant 1006046 (DMS). 2000 NDSEG Graduate Fellowship. 1998 British Marshall Scholarship. 1998 Valedictorian, Princeton University, Class of 1998. Invited talks since 2011 Multi-lecture series are listed in bold. 2018 Perimeter (Higher Algebra in Mathematical Physics). 2018 Sendai (String-Math 2018). 2018 CIRM, Marseilles (Vector Bundles over Algebraic Curves). 2018 Michigan State University (Cluster Algebras and Mathematical Physics). 2018 G¨ottingen(Gauge theory and Geometry): Four lectures. 2018 University of Maryland (math seminar). 2017 Yale (math department colloquium). 2017 Rice (math department colloquium). -
Booklet (Page 1)
I NSTITUTE for ADVANCED STUDY 2006–2007 FACULTY AND MEMBERS PRINCETON • NEW JERSEY I NSTITUTE FOR ADVANCED STUDY Since its founding, the Institute has maintained a policy of non-discrimination. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to pro- mote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. —Louis Bamberger and Caroline Bamberger Fuld, in a letter, dated June 4, 1930, to the Institute’s Trustees. 2 I NSTITUTE FOR ADVANCED STUDY CONTENTS Institute Mission and History . 4 School of Historical Studies . 6 School of Mathematics . 24 School of Natural Sciences . 43 School of Social Science . 58 Program in Interdisciplinary Studies . 68 Artist-in-Residence Program . 70 Director’s Visitors . 71 Trustees and Officers of the Board and of the Corporation . 72 Administration . 76 Past Directors and Faculty . 79 Index . 80 3 I NSTITUTE FOR ADVANCED STUDY INSTITUTE FOR ADVANCED STUDY MISSION AND HISTORY The Institute for Advanced Study is one of the world’s leading centers for theoretical research and intellectual inquiry. The Institute exists to encourage and support fundamental scholarship—the original, often speculative, thinking that produces advances in knowledge.