Andrew Wiles Wins the 2016 Abel Prize for His Proof of Fermat's Last Theorem
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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). -
APRIL 2014 ● Official Newsletter of the LSU College of Science E-NEWS
APRIL 2014 ● Official newsletter of the LSU College of Science e-NEWS NEWS/EVENTS LSU Museum of Natural Science Research Shows Hummingbird Diversity Is Increasing Research relying heavily on the genetic tissue collection housed at LSU’s Museum of Natural Science (one of the world’s largest collections of vertebrate tissues) has provided a newly constructed family tree of hummingbirds, with the research demonstrating that hummingbird diversity appears to be increasing rather than reaching a plateau. The work, started more than 12 years ago at LSU, culminated with a publication in the journal Current Biology. - LSU Office of Research Communications More LSU Geologist's Innovative Use of Magnetic Susceptibility Helps Uncover Burial Site of Notorious Texas Outlaw Brooks Ellwood, Robey H. Clark Distinguished Professor of Geology & Geophysics, was featured in a recent edition of Earth, for his innovative use of magnetic susceptibility (MS) for high- resolution interpretation of sedimentary sequences. Magnetic susceptibility is essentially how easily a material is magnetized in an inducing magnetic field. MS has proved useful for dating archeological sites more than 40,000 years old. One of Ellwood's more unusual applications of MS was when he was approached by Doug Owsley, forensic anthropologist at the Smithsonian Institution, to help search for the burial site of notorious Texas outlaw William Preston Longley, or 'Wild Bill." Ellwood, Owsley and their research team excavate the grave site of More "Wild Bill." LSU Alum, MacArthur Fellow Susan Murphy Gives Porcelli Lectures LSU mathematics graduate and 2013 MacArthur Fellow Susan Murphy was the featured speaker for the 2014 Porcelli Lectures held April 28 in the LSU Digital Media Center. -
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. -
Number Theory, Analysis and Geometry
Number Theory, Analysis and Geometry Dorian Goldfeld • Jay Jorgenson • Peter Jones Dinakar Ramakrishnan • Kenneth A. Ribet John Tate Editors Number Theory, Analysis and Geometry In Memory of Serge Lang 123 Editors Dorian Goldfeld Jay Jorgenson Department of Mathematics Department of Mathematics Columbia University City University of New York New York, NY 10027 New York, NY 10031 USA USA [email protected] [email protected] Peter Jones Dinakar Ramakrishnan Department of Mathematics Department of Mathematics Yale University California Institute of Technology New Haven, CT 06520 Pasadena, CA 91125 USA USA [email protected] [email protected] Kenneth A. Ribet John Tate Department of Mathematics Department of Mathematics University of California at Berkeley Harvard University Berkeley, CA 94720 Cambridge, MA 02138 USA USA [email protected] [email protected] ISBN 978-1-4614-1259-5 e-ISBN 978-1-4614-1260-1 DOI 10.1007/978-1-4614-1260-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011941121 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. -
Pierre Deligne
www.abelprize.no Pierre Deligne Pierre Deligne was born on 3 October 1944 as a hobby for his own personal enjoyment. in Etterbeek, Brussels, Belgium. He is Profes- There, as a student of Jacques Tits, Deligne sor Emeritus in the School of Mathematics at was pleased to discover that, as he says, the Institute for Advanced Study in Princeton, “one could earn one’s living by playing, i.e. by New Jersey, USA. Deligne came to Prince- doing research in mathematics.” ton in 1984 from Institut des Hautes Études After a year at École Normal Supériure in Scientifiques (IHÉS) at Bures-sur-Yvette near Paris as auditeur libre, Deligne was concur- Paris, France, where he was appointed its rently a junior scientist at the Belgian National youngest ever permanent member in 1970. Fund for Scientific Research and a guest at When Deligne was around 12 years of the Institut des Hautes Études Scientifiques age, he started to read his brother’s university (IHÉS). Deligne was a visiting member at math books and to demand explanations. IHÉS from 1968-70, at which time he was His interest prompted a high-school math appointed a permanent member. teacher, J. Nijs, to lend him several volumes Concurrently, he was a Member (1972– of “Elements of Mathematics” by Nicolas 73, 1977) and Visitor (1981) in the School of Bourbaki, the pseudonymous grey eminence Mathematics at the Institute for Advanced that called for a renovation of French mathe- Study. He was appointed to a faculty position matics. This was not the kind of reading mat- there in 1984. -
On Elliptic Curves of Conductor N=PQ
On Elliptic Curves of Conductor N=PQ Item Type text; Electronic Thesis Authors Howe, Sean Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 30/09/2021 23:14:58 Item License http://rightsstatements.org/vocab/InC/1.0/ Link to Item http://hdl.handle.net/10150/146586 ON ELLIPTIC CURVES OF CONDUCTOR N=PQ SEAN HOWE (DRAFT OF 3 MAY 2010) Abstract. We study elliptic curves with conductor N = pq for p and q prime. By studying the 2-torsion eld we obtain that for N a product of primes satisfying some congruency conditions and class number conditions on related quadratic elds, any elliptic curve of conductor N has a rational point of order 2. By studying a minimal Weierstrass equation and its discriminant we obtain a solution to some Diophantine equation from any curve with conductor N = pq and a rational point of order 2. Under certain congruency conditions, this equation has no solutions, and so we conclude that in this situation there is no elliptic curve of conductor N with a rational point of order 2. Combining these two results, we prove that for a family of N = pq satisfying more specic congruency conditions and class number conditions on related quadratic elds, there are no elliptic curves of conductor N. We use a computer to nd all N < 107 satisfying these conditions, of which there are 67. -
Tate Receives 2010 Abel Prize
Tate Receives 2010 Abel Prize The Norwegian Academy of Science and Letters John Tate is a prime architect of this has awarded the Abel Prize for 2010 to John development. Torrence Tate, University of Texas at Austin, Tate’s 1950 thesis on Fourier analy- for “his vast and lasting impact on the theory of sis in number fields paved the way numbers.” The Abel Prize recognizes contributions for the modern theory of automor- of extraordinary depth and influence to the math- phic forms and their L-functions. ematical sciences and has been awarded annually He revolutionized global class field since 2003. It carries a cash award of 6,000,000 theory with Emil Artin, using novel Norwegian kroner (approximately US$1 million). techniques of group cohomology. John Tate received the Abel Prize from His Majesty With Jonathan Lubin, he recast local King Harald at an award ceremony in Oslo, Norway, class field theory by the ingenious on May 25, 2010. use of formal groups. Tate’s invention of rigid analytic spaces spawned the John Tate Biographical Sketch whole field of rigid analytic geometry. John Torrence Tate was born on March 13, 1925, He found a p-adic analogue of Hodge theory, now in Minneapolis, Minnesota. He received his B.A. in called Hodge-Tate theory, which has blossomed mathematics from Harvard University in 1946 and into another central technique of modern algebraic his Ph.D. in 1950 from Princeton University under number theory. the direction of Emil Artin. He was affiliated with A wealth of further essential mathematical ideas Princeton University from 1950 to 1953 and with and constructions were initiated by Tate, includ- Columbia University from 1953 to 1954.