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A Note on the Origin of the Twin Prime Conjecture
A Note on the Origin of the Twin Prime Conjecture by William Dunham Department of Mathematics & Computer Science, Muhlenberg College; Department of Mathematics, Harvard University (visiting 2012-2013) More than any other branch of mathematics, number As the title suggests, de Polignac’s paper was about theory features a collection of famous problems that took prime numbers, and on p. 400 he stated two “theorems.” centuries to be proved or that remain unresolved to the It should be noted that he was not using the word in its present day. modern sense. Rather, de Polignac confirmed the truth of Among the former is Fermat’s Last Theorem. This these results by checking a number of cases and thereby states that it is impossible to find a whole number n ≥ 3 called them “theorems.” Of course, we would call them, at and whole numbers x , y , and z for which xn + yn = zn . best, “conjectures.” The true nature of these statements is suggested by the fact that de Polignac introduced them In 1640, as all mathematicians know, Fermat wrote this in under the heading “Induction and remarks” as seen below, a marginal note and claimed to have “an admirable proof” in a facsimile of his original text. that, alas, did not fit within the space available. The result remained unproved for 350 years until Andrew Wiles, with assistance from Richard Taylor, showed that Fermat was indeed correct. On the other hand, there is the Goldbach conjecture, which asserts that every even number greater than 2 can be expressed as the sum of two primes. -
For Your Information
fyi.qxp 3/18/98 3:19 PM Page 244 For Your Information structure federal support. The study is part of a larger ef- International Study of fort at the Academy to gauge where the U.S. stands in- Mathematics and Science ternationally in scientific research. The motivation comes from a 1993 report by the Committee on Science, Engi- Achievement neering, and Public Policy (COSEPUP), which set forth strate- gies for making decisions about how best to use federal The first installment of results from the Third International research funds. COSEPUP is a committee of the NAS, the Mathematics and Science Study (TIMSS) was released on No- National Academy of Engineering, and the Institute of Med- vember 20. This first batch of data pertains to achievement icine. The COSEPUP report recommended that the U.S. aim of eighth-graders; later releases will focus on fourth- and to be the world leader in certain critical fields and to be twelfth-graders. The study found that U.S. eighth-graders among the leaders in other areas. The report urged field- performed below the international average in mathemat- by-field assessments by independent panels of researchers ics but slightly above average in science. The U.S. was in the field, researchers in closely related fields, and users among thirty-three countries in which there was no sta- of the research. The mathematical sciences study is the first tistically significant difference between the performance such assessment. If this project is successful, the Academy of eighth-grade boys and girls in mathematics. The study will follow suit with other areas. -
Spring 2014 Fine Letters
Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544 Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize. -
Selected Papers
Selected Papers Volume I Arizona, 1968 Peter D. Lax Selected Papers Volume I Edited by Peter Sarnak and Andrew Majda Peter D. Lax Courant Institute New York, NY 10012 USA Mathematics Subject Classification (2000): 11Dxx, 35-xx, 37Kxx, 58J50, 65-xx, 70Hxx, 81Uxx Library of Congress Cataloging-in-Publication Data Lax, Peter D. [Papers. Selections] Selected papers / Peter Lax ; edited by Peter Sarnak and Andrew Majda. p. cm. Includes bibliographical references and index. ISBN 0-387-22925-6 (v. 1 : alk paper) — ISBN 0-387-22926-4 (v. 2 : alk. paper) 1. Mathematics—United States. 2. Mathematics—Study and teaching—United States. 3. Lax, Peter D. 4. Mathematicians—United States. I. Sarnak, Peter. II. Majda, Andrew, 1949- III. Title. QA3.L2642 2004 510—dc22 2004056450 ISBN 0-387-22925-6 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. 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, Inc., 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. Printed in the United States of America. -
Dr. Yitang Zhang Professor Department of Mathematics University of California, Santa Barbara
Distinguished Lifetime Achievement Award Dr. Yitang Zhang Professor Department of Mathematics University of California, Santa Barbara Citation of Accomplishments Establishing the first finite bound on the gaps of prime numbers and thus solving a centuries- old problem in number theory, and his unsubdued passion for mathematics and science. Dr. Yitang Zhang was born on February 5, 1955 in Shanghai, China, and lived there until he was 13 years old. During the Cultural Revolution, he and his parents were sent to the countryside to work in the fields. He worked as a laborer for ten years and was unable to attend high school. After the Cultural Revolution ended, he entered Peking University in 1978 as an undergraduate student and graduated in 1982. Then he became a graduate student of Professor Pan Chengbiao, a number theorist at Peking University, and obtained his master’s degree in mathematics in 1984. With recommendations from Professor Ding Shisun, the president of Peking University, Yitang was granted a full scholarship at Purdue University. He arrived at Purdue in June 1985, studied there for seven years, and obtained his Ph.D. in mathematics in December 1991. After graduation, he had a hard time finding an academic position. After several years, he managed to find a position as a lecturer at the University of New Hampshire (UNH), where he was hired by Professor Kenneth Appel in 1999. He served as a lecturer at UNH until January 2014, when UNH appointed him to a full professorship as a result of his breakthrough on the distribution of prime numbers. In Fall 2015, he accepted an offer of full professorship at the University of California, Santa Barbara. -
(November 12-13)- Page 545
College Park Program (October 30-31) - Page 531 Baton Rouge Program (November 12-13)- Page 545 Notices of the American Mathematical Society < 2.. c: 3 ('1) ~ z c: 3 C" ..,('1) 0'1 October 1982, Issue 220 Volume 29, Number 6, Pages 497-616 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitred on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. -
Child of Vietnam War Wins Top Maths Honour 19 August 2010, by P.S
Child of Vietnam war wins top maths honour 19 August 2010, by P.S. Jayaram Vietnamese-born mathematician Ngo Bao Chau Presented every four years to two, three, or four on Thursday won the maths world's version of a mathematicians -- who must be under 40 years of Nobel Prize, the Fields Medal, cementing a journey age -- the medal comes with a cash prize of 15,000 that has taken him from war-torn Hanoi to the Canadian dollars (14,600 US dollars). pages of Time magazine. The only son of a physicist father and a mother who Ngo, 38, was awarded his medal in a ceremony at was a medical doctor, Ngo's mathematical abilities the International Congress of Mathematicians won him a place, aged 15, in a specialist class of meeting in the southern Indian city of Hyderabad. the Vietnam National University High School. The other three recipients were Israeli In 1988, he won a gold medal at the 29th mathematician Elon Lindenstrauss, Frenchman International Mathematical Olympiad and repeated Cedric Villani and Swiss-based Russian Stanislav the same feat the following year. Smirnov. After high school, he was offered a scholarship by Ngo, who was born in Hanoi in 1972 in the waning the French government to study in Paris. He years of the Vietnam war, was cited for his "brilliant obtained a PhD from the Universite Paris-Sud in proof" of a 30-year-old mathematical conundrum 1997 and became a professor there in 2005. known as the Fundamental Lemma. Earlier this year he became a naturalised French The proof offered a key stepping stone to citizen and accepted a professorship at the establishing and exploring a revolutionary theory University of Chicago. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Prizes and Awards
DENVER • JAN 15–18, 2020 January 2020 Prizes and Awards 4:25 PM, Thursday, January 16, 2020 PROGRAM OPENING REMARKS Michael Dorff, Mathematical Association of America AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society BÔCHER MEMORIAL PRIZE American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY American Mathematical Society LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society JOSEPH L. DOOB PRIZE American Mathematical Society LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics CHAUVENET PRIZE Mathematical Association of America DAVID P. R OBBINS PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y. HU AWARD FOR DISTINGUISHED SERVICE TO MATHEMATICS Mathematical Association of America CLOSING REMARKS Jill C. -
Phillip Augustus Griffiths 1962 Princeton University
Pyung-Lyun Kang 1988 University of Pennsylvania Lakshmi Modali 1996 Syracuse University J. Travis Lee Tony Horowitz 2004 Syracuse University 1982 Brown University Nicolò Fontana Tartaglia Philip Joseph Lynn Steven P. Diaz 2006 Syracuse University 1982 Brown University Thomas Bleier 2011 Syracuse University Ostilio Ricci Seonja Kim Universita' di Brescia 1989 Seoul National University Seong Suk Park 2002 Seoul National University Changho Keem 1983 Brown University Galileo Galilei Young Rock Kim 1585 Università di Pisa Vittorio Perduca 2003 Seoul National University 2009 Università di Torino Antonella Grassi Colin Diemer 1990 Duke University 2010 University of Pennsylvania Dong-Kwan Shin Benedetto Castelli 1990 Duke University 1610 Università degli Studi di Padova Qi Zhang 1990 Duke University Yun-Gang Ye Evangelista Torricelli Marin Mersenne Nora Youngs 1991 Duke University Università di Roma La Sapienza 1611 Université de Paris 2014 University of Nebraska-Lincoln Yiannis Vlassopoulos Caitlyn Parmelee 1998 Duke University 2016 University of Nebraska-Lincoln Richard Paul Horja 1999 Duke University Christopher Austin Frederick Vincenzo Viviani Gilles Personne de Roberval 2008 Colorado State University Carina Curto David Robert Morrison 1642 Università di Pisa Elin Rose Smith 2005 Duke University 1980 Harvard University Russell Richins 2010 University of Utah 2010 Colorado State University Charlie Ronald Beil Justin D. Marks 2010 University of California, Santa Barbara Cheryl B. Percell Hwan Yong Lee 1989 Rice University 2010 University of -
Ten Mathematical Landmarks, 1967–2017
Ten Mathematical Landmarks, 1967{2017 MD-DC-VA Spring Section Meeting Frostburg State University April 29, 2017 Ten Mathematical Landmarks, 1967{2017 Nine, Eight, Seven, and Six Nine: Chaos, Fractals, and the Resurgence of Dynamical Systems Eight: The Explosion of Discrete Mathematics Seven: The Technology Revolution Six: The Classification of Finite Simple Groups Ten Mathematical Landmarks, 1967{2017 Five: The Four-Color Theorem 1852-1976 1852: Francis Guthrie's conjecture: Four colors are sufficient to color any map on the plane in such a way that countries sharing a boundary edge (not merely a corner) must be colored differently. 1878: Arthur Cayley addresses the London Math Society, asks if the Four-Color Theorem has been proved. 1879: A. B. Kempe publishes a proof. 1890: P. J. Heawood notes that Kempe's proof has a serious gap in it, uses same method to prove the Five-Color Theorem for planar maps. The Four-Color Conjecture remains open. 1891: Heawood makes a conjecture about coloring maps on the surfaces of many-holed tori. 1900-1950's: Many attempts to prove the 4CC (Franklin, George Birkhoff, many others) give a jump-start to a certain branch of topology called Graph Theory. The latter becomes very popular. Ten Mathematical Landmarks, 1967{2017 Five: The Four-Color Theorem (4CT) The first proof By the early 1960s, the 4CC was proved for all maps with at most 38 regions. In 1969, H. Heesch developed the two main ingredients needed for the ultimate proof, namely reducibility and discharging. He also introduced the idea of an unavoidable configuration. -
Awards of ICCM 2013 by the Editors
Awards of ICCM 2013 by the Editors academies of France, Sweden and the United States. He is a recipient of the Fields Medal (1986), the Crafoord Prize Morningside Medal of Mathematics in Mathematics (1994), the King Faisal International Prize Selection Committee for Science (2006), and the Shaw Prize in Mathematical The Morningside Medal of Mathematics Selection Sciences (2009). Committee comprises a panel of world renowned mathematicians and is chaired by Professor Shing-Tung Björn Engquist Yau. A nomination committee of around 50 mathemati- Professor Engquist is the Computational and Applied cians from around the world nominates candidates based Mathematics Chair Professor at the University of Texas at on their research, qualifications, and curriculum vitae. Austin. His recent work includes homogenization theory, The Selection Committee reviews these nominations and multi-scale methods, and fast algorithms for wave recommends up to two recipients for the Morningside propagation. He is a member of the Royal Swedish Gold Medal of Mathematics, up to two recipients for the Morningside Gold Medal of Applied Mathematics, and up to four recipients for the Morningside Silver Medal of Mathematics. The Selection Committee members, with the exception of the committee chair, are all non-Chinese to ensure the independence, impartiality and integrity of the awards decision. Members of the 2013 Morningside Medal of Mathe- matics Selection Committee are: Richard E. Borcherds Professor Borcherds is Professor of Mathematics at the University of California at Berkeley. His research in- terests include Lie algebras, vertex algebras, and auto- morphic forms. He is best known for his work connecting the theory of finite groups with other areas in mathe- matics.