FOCUS May/June 2004 FOCUS is published by the Mathematical Association of America in January, February, March, April, May/June, FOCUS August/September, October, November, and December. Volume 24 Issue 5 Editor: Fernando Gouvêa, Colby College; [email protected] Managing Editor: Carol Baxter, MAA Inside [email protected] Senior Writer: Harry Waldman, MAA [email protected] 4 Convergence: A New Online Magazine from the MAA Please address advertising inquiries to: By Victor Katz Frank Peterson [email protected] President: Ronald L. Graham 5 SIGMAA QL is Formed By Rick Gillman President-Elect: Carl C. Cowen First Vice-President: Barbara T. Faires, 6 The Archives of Mathematics at the Center for American History Second Vice-President: Jean Bee Chan, By Kristy Sorensen Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: John W. Kenelly 8 The Teacher as Artist: A Letter to My Colleagues Executive Director: Tina H. Straley By Peter Taylor Associate Executive Director and Director of Publications: Donald J. Albers 10 What I Learned by Teaching Proof and Logic By Peter Ruane FOCUS Editorial Board: Rob Bradley; J. Kevin Colligan; Sharon Cutler Ross; Joe Gallian; Jackie Giles; Maeve McCarthy; Colm 12 Mathematics Magazine Editor Search Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. 13 2004 Summer Short Course—Teaching and Doing Knot Theory Letters to the editor should be addressed to Fernando Gouvêa, Colby College, Dept. of 14 Remembering Bill Chinn Mathematics, Waterville, ME 04901, or by email to [email protected]. By Jean Bee Chan Subscription and membership questions should be directed to the MAA Customer 15 Letters to the Editor Service Center, 800-331-1622; e-mail: [email protected]; (301) 617-7800 (outside 16 MAA Contributed Paper Sessions: U.S. and Canada); fax: (301) 206-9789. MAA Atlanta Joint Mathematics Meeting, January 5-8, 2005 Headquarters: (202) 387-5200. Copyright © 2004 by the Mathematical 21 MAA President Ronald L. Graham Testifies Before House Association of America (Incorporated). Educational institutions may reproduce Appropriations Subcommittee on Funding for articles for their own use, but not for sale, Mathematics Education provided that the following citation is used: By Harry Waldman “Reprinted with permission of FOCUS, the newsletter of the Mathematical Association of America (Incorporated).” On the cover: The MAA has just launched Convergence, an online magazine about the History of Mathematics. See the article on page 4. Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. FOCUS Deadlines Box 90973, Washington, DC 20090-0973. August/September October November ISSN: 0731-2040; Printed in the United States Editorial Copy July 8 September 16 of America. Display Ads July 9 August 20 September 24 Employment Ads June 11 August 13 September 10 2 FOCUS Sir Michael Atiyah and Prof. Isadore Singer Win the 2004 Abel Prize The Norwegian Academy of Sciences and Letters has awarded the 2004 Abel Prize jointly to Sir Michael Francis Atiyah, of the University of Edinburgh, and Isadore M. Singer, of the Massachu- setts Institute of Technology. Atiyah and Singer will receive the prize, wrote the Academy, “for their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theo- retical physics.” The Atiyah-Singer Index Isadore M. Singer Theorem is considered one of the great Sir Michael Francis Atiyah landmarks of twentieth-century math- ematics, influencing many of the most as one of their most important contri- Michael Francis Atiyah was born in 1929 important developments in topology, butions. in London and was educated at Trinity differential geometry, and quantum field College, Cambridge. He spent most of his theory. An account of the theorem aimed Isadore M. Singer was born in 1924 in career at Cambridge and Oxford. He oc- at a general mathematical public can be Detroit and was educated at the Univer- cupied the famous Savilian Chair of Ge- found on the Abel Prize web site at http:/ sity of Michigan and the University of ometry at Oxford and later was Master /www.abelprisen.no/nedlastning/2004/ Chicago. He joined the faculty at the of Trinity College in Cambridge. popular_english_2004.pdf. Massachusetts Institute of Technology in 1950, and has been there ever since. He While in Cambridge, he helped create the A few decades ago, physicist Freeman has received several prizes for his work, Isaac Newton Institute for Mathemati- Dyson pointed out that “the marriage including the Steele Prize for Lifetime cal Sciences and became its first direc- between mathematics and physics, which Achievement. Accepting that prize, he tor. Atiyah received the Fields Medal in was so enormously fruitful in past cen- said, “For me the classroom is an impor- 1966. He has been Sir Michael Atiyah turies, has recently ended in divorce.” The tant counterpart to research. I enjoy since 1983, and was made a member of situation has changed dramatically since teaching undergraduates at all levels, and the Order of Merit in 1992. then; Dyson’s “divorce” turned out to be I have a host of graduate students, many only a temporary separation. Atiyah and of whom have ended up teaching me For more information on the Abel Prize Singer, both jointly and individually, have more than I have taught them.” Singer and on this year’s winners, visit http:// been instrumental in repairing the rift, has also written several important text- www.abelprisen.no/en. See also the April and the Norwegian Academy noted this books. 2004 Devlin’s Angle on the MAA web site. An Update on Hales’ Proof of Kepler’s Conjecture In 1998, Thomas C. Hales announced it. An attempt to check everything by per will be split in two parts. The more that he had proved Kepler’s Conjecture hand ended badly: “[The referees] have theoretical part will be published by the about the best possible sphere packing not been able to certify the correctness Annals and the computer-intensive part in three-dimensional space. His claim of the proof, and will not be able to cer- will be published in another journal, Dis- generated controversy, mostly because of tify it in the future, because they have run crete and Computational Geometry. the crucial role of computers in the (very out of energy to devote to the problem,” long) proof. As Hales says in the most said Annals editor Robert McPherson. Hales himself has opted for a more radi- recent version, “nearly every aspect of the The Annals then considered publishing cal route. He has started the Flyspeck proof relies on computer verification.” the paper with a disclaimer, to the effect Project, an attempt to create a formal The issue was put into sharp relief by the that the editors could not certify that proof of Kepler’s Conjecture. The idea is editors of the Annals of Mathematics, who every detail was correct. to create (via computer) a version of the were leery of publishing a paper whose proof of the conjecture that can be au- correctness they could not verify. An article in the April 6 issue of The New tomatically verified line-by-line. You can York Times, entitled “In Math, Comput- read more about this at http:// The problem, for the editors, was to what ers Don’t Lie. Or Do They?,”reports that www.math.pitt.edu/~thales/flyspeck/ extent they should trust mathematics the Annals editors have decided to solve index.html. done on the computer without checking the problem in a different way. The pa- 3 FOCUS May/June 2004 Convergence: A New Online Magazine from the MAA By Victor Katz The MAA announced the launching of magazine will report on past meetings a new online magazine on the history of and give notice of future meetings. mathematics and its use in teaching, en- Where abstracts are available for a par- titled Convergence: Where Mathematics, ticular meeting, these will be included. History and Teaching Interact, with the We may also include copies of handouts financial support of the National Science for easy access, as well as links to the Foundation. The target audience is author’s webpage, if available. teachers of grades 9-14 mathematics, be they secondary teachers, two- or four- Initially the magazine will be free to all. year college teachers, or college teachers However, a subscription fee will be nec- preparing secondary teachers. (“Grade essary after the initial period. We hope 9–14 mathematics” encompasses algebra, Frank Swetz and Victor Katz to secure institutional as well as personal synthetic and analytic geometry, trigo- Reviews of current and past books, ar- subscriptions. Information as to cost and nometry, probability and statistics, el- ticles, and teaching aids on the history access will be provided on the Conver- ementary functions, calculus, linear al- of mathematics of use to teachers, as well gence site shortly. gebra, and differential equations.) The as reviews of websites providing infor- initial editors of the magazine are Victor mation on the history of mathematics. Currently, we have a limited supply of J. Katz, from the University of the Dis- articles in our pipeline. Because our goal trict of Columbia, and Frank Swetz, from Classroom suggestions. These may be self- is to bring out new material on a regular Penn State University, Harrisburg. contained articles showing how to use basis, we need a continual flow of articles history in the teaching of a particular and classroom suggestions. We therefore Among the types of material that will topic or they may be materials closely welcome your ideas for articles as well as appear in the magazine are the follow- related to a main article, showing in some your completed manuscripts.