FOCUS November 2006 InProfessors honor Bert K. Waits of and Franklintheir Demana extraordinary have made an indelible impact achievements. on mathematics education, hundreds of thousands of educators and countless students around the world. In addition to pioneering the use of graphing calculators to enhance classroom instruction, Bert and Frank co-founded the T3 • Teachers Teaching with Technology™ educator professional development organization and the highly-regarded T3 International Conference. The annual Demana-Waits Scholarship for Future Teachers, supported by Texas Instruments, continues to help college students pursue a teaching career in secondary school mathematics. Bert and Frank’s long list of accomplishments reflects their devotion to furthering mathematics education. We are proud to have shared their vision, having worked closely together in the development of TI’s first graphing calculator. Bert and Frank’s passion for teaching and learning mathematics through “the power of visualization” continues to inspire all that we do at TI and is sure to carry on for future generations of educators and students. Please join us in thanking them for their contributions and lasting legacy. Visit education.ti.com/us/bertandfrank. AD7039 © 2006 Texas Instruments November 2006 FOCUS FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, May/June, August/September, October, November, and December. Editor: Fernando Gouvêa, Colby College; Volume 26 Issue 8 [email protected] Managing Editor: Carol Baxter, MAA Inside [email protected] Senior Writer: Harry Waldman, MAA hwald- 4 Paul Halmos: A Life in Mathematics [email protected] 5 Terence Tao Receives the MacArthur Fellowship Please address advertising inquiries to: Re- becca Hall [email protected] 5 NCTM Releases “Curriculum Focal Points” President: Carl C. Cowen 6 Fields Medals and Other Awards Announced at the 2006 International First Vice-President: Barbara T. Faires, Congress of Mathematicians Second Vice-President: Jean Bee Chan, 7 The Press is Fascinated by Perelman Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 9 Institute in the History of Mathematics and Its Use in Teaching: John W. Kenelly Ten Years After Executive Director: Tina H. Straley 12 Alice in NUMB3Rland FOCUS Editorial Board: Rob Bradley; J. Kevin Colligan; Sharon Cutler Ross; Joe 14 Archives of American Mathematics Spotlight: The Alfred Schild Papers Gallian; Jackie Giles; Maeve McCarthy; 16 Removal From Office: A Proposed Addition to the MAA Bylaws Colm Mulcahy; Peter Renz; Annie Selden; Hortensia Soto-Johnson; Ravi Vakil. 18 Mathematics Teaching and American Competitiveness Letters to the editor should be addressed to 19 Teaching Time Savers: Reviewing Homework Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by 20 What I Learned About the Process of Change: email to [email protected]. A College Instructor’s Reflections Subscription and membership questions 23 MathFest 2006, Knoxville, Tennessee should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 24 MathFest 2006 in Pictures [email protected]; (01) 617-7800 (outside U.S. and Canada); fax: (01) 06-9789. MAA 26 MAA Prizes and Awards Announced at MathFest 2006 Headquarters: (0) 87-500. 28 Gödel’s Contributions to the Foundations of Mathematics: An Overview Copyright © 005 by the Mathematical Association of America (Incorporated). 30 Richard Anderson is the Newest Member of the Icosahedron Society Educational institutions may reproduce articles 31 Curve Sketching: A Disappearing Delight for their own use, but not for sale, provided that the following citation is used: “Reprinted 32 2006—The Year of the Dog with permission of FOCUS, the newsletter An Auspicious Time for the MAA’s Study Tour to China of the Mathematical Association of America (Incorporated).” 36 Letters to the Editor Periodicals postage paid at Washington, DC and 38 William F. Lucas Fund Presents Short Course at MathFest additional mailing offices.Postmaster: Send address changes to FOCUS, Mathematical 39 PMET Returns to Texas Southern Univeristy Association of America, P.O. Box 9097, 40 A Report on the Mathematics Geneaolgy Project Washington, DC 0090-097. ISSN: 071-040; Printed in the United States 42 Call for Proposals of America. 43 Report Card: College Education is not Affordable for Most Americans 44 Employment Opportunities On the cover: Terence Tao, winner of the Fields Medal and a MacArthur Fellow- ship. Photograph courtesy of UCLA. FOCUS November 2006 Paul R. Halmos (1916-2006) statements like these. He knew what he was doing; he was provoking discussion. And provoke discussion he did. aul Richard Halmos, a major figure in P Influential in the mathematical world, he American mathematics died on October served as Vice President (1981-8) and , 006 in San Jose, California, after a subsequently on the Council of the Amer- short illness. Renowned as a mathemati- ican Mathematical Society (AMS) and cal researcher principally in the areas on the Board of Governors of the MAA. of operator theory, ergodic theory and For his outstanding work in mathematics algebraic logic, but also in probability he was awarded the prestigious Leroy and statistics, topological groups, and P. Steele Prize of the AMS and the Dis- Boolean algebras, he was also one of the tinguished Service Award of the MAA. pre-eminent mathematical expositors of For his writing he won the Chauvenet his day, having written a series of classic Prize, two Lester R. Ford Awards, and texts: Finite-Dimensional Vector Spaces, the George Pólya Award, all from the Measure Theory, A Hilbert Space Prob- MAA. He served a five-year term as lem Book, Naïve Set Theory, Problems editor of the American Mathematical for Mathematicians Young and Old, to Monthly and held editorial positions for name only a few. These works of his and Mathematical Reviews, the Proceedings others inspired generations of students to of the American Mathematical Society, pursue careers in mathematics. Paul Halmos the Journal fűr die reine und angewandte Mathematik, and the Indiana Journal of Born in Budapest, Hungary, on March raphy, and a pioneering volume, I Have Mathematics. He also edited five book , 1916, Halmos at the age of 1 came a Photographic Memory, a record of a series for Springer Verlag: Universitexts, with his family to Chicago. He attended lifetime of taking pictures of mathemati- the Ergebnisse der Mathematik, Problem high school there and later enrolled at the cians. Books, Undergraduate Texts and Gradu- University of Illinois at Urbana-Cham- ate Texts in Mathematics. paign, from which he received his PhD As a teacher he was extraordinarily ef- in 198, under the supervision of Joseph fective, usually using a modified Moore Though he had roots in Hungary, he Doob. From there he went to the Institute method to encourage student participa- always thought of himself as an Ameri- for Advanced Study in Princeton for two tion in the discovery of mathematics. For can mathematician. Hungary neverthe- years, where he served as assistant to this he was awarded the Haimo Award less honored him with membership in John von Neumann. After his years at the for Distinguished College or University the Hungarian Academy of Sciences. Institute he moved to academic positions Teaching of Mathematics by the Math- Further, he was elected to membership at Syracuse University; the University ematical Association of America (MAA) in the Royal Society of Edinburgh. He of Chicago; the University of Michigan, in 1994. held honorary doctorates from St. An- Ann Arbor; the University of Hawaii; the drews University, DePauw University, University of California at Santa Barbara; For the clarity of his writing and his lec- Kalamazoo College, and the University Indiana University; and Santa Clara Uni- tures he was even more widely admired. of Waterloo. Among his honors were a versity from which he retired in 1995. He His work was often witty and colorful, Guggenheim Fellowship. had also held visiting appointments at indeed provocative at times, but always Harvard University, Tulane University, well-planned and polished. When asked In recent years Halmos and his wife of the University of Montevideo, the Uni- about the importance of computers, he 60 years, Virginia, were recognized for versity of Miami (Florida), the University replied that they are important, but not their philanthropy. In 00 they gave a of California at Berkeley, the University to mathematics. He then proceeded to $,000,000 gift to the MAA to develop an of Washington (Seattle), the University explain why. And he actually wrote an existing building in Washington, DC, to of Edinburgh, Chiao Tung University in article entitled “Applied mathematics become a meetings center. Already in use Taiwan, and the University of Western is bad mathematics.” Asked about this, for various mathematical activities, the Australia. he first replied, “First it is. Second it center will be dedicated in April 007. In isn’t . [Applied mathematics] is a addition they endowed book prize funds A brilliant writer and lecturer, Halmos good contribution. It serves humanity. It for both the AMS and the MAA. not only wrote roughly 100 research pa- solves problems . but much too often pers, but also 16 books and many book it is bad, ugly, badly arranged, sloppy, Halmos is survived by his wife, Virginia, reviews. Several of his books are easily untrue, undigested, unorganized, and of Los Gatos, California, and a cousin, accessible to a non-specialist audience, unarchitected mathematics.” Those who Ferenc Halmos, of Budapest. In line notably, his memoirs, entitled I Want to knew him learned to check for that mis- with Halmos’s request, no services are Be a Mathematician: an Automathog- chievous look in his eye when he made planned. 4 November 2006 FOCUS Terence Tao Receives MacArthur Fellowship Terence Tao is on a hot streak. In the his PhD from Princeton in 1996 and is The MacArthur Fellowships are unre- space of a few months he has won a now Professor of Mathematics at the stricted grants awarded to brilliant and Fields Medal (see page 6), published a University of California Los Angeles.