THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA August 1996 u.s. Team Places Second at 1996 IMO Competing against teams representing a Volume 16, Number 4 record seventy-five countries, a team of six American high school students came in sec­ ond, winning six medals at the thirty-seventh In this Issue International Mathematical Olympiad held in Bombay, India. The top five teams and their scores (out of a 4 Quantitative possible 252) were Romania (187), U.S.A. The 1996 USAMO Team with members ofthe USAMO Reasoning (185), Hungary (167), Russia (162), and the committee and the coaches. United Kingdom (161). Nathan G. Curtis, Thomas Jefferson High 6 A Visit to the The U.S. team was chosen on the basis of School for Science and Technology, Alexan­ their performance in the twenty-fifth annual Fifth Grade dria, VA, silver medalist U.S.A. Mathematical Olympiad (USAMO) 12 Section Awards held in May. (For more information on the Michael R. Korn, Mounds View High School, USAMO, see page 3.) Arden Hills, MN, gold medalist for Distinguished Teaching IMO team members include: CarlA. Miller, Montgomery Blair High School, Silver Spring, MD, silver medalist Carl J. Bosley, Washburn Rural High School, 15 MAA Annual Topeka, KS, gold medalist Alexander H. Saltman, Science Academy at LBJ, Austin, TX, gold medalist Report Christopher C. Chang, Henry M. Gunn High School, Palo Alto, CA, gold medalist More details can be found on MAA Online 29 Register Early (http://www.maa.org/). for the Joint Mathematics Smale and Karp Awarded National Medal of Science Meetings Mathematician Stephen Smale and computer Richard M. Karp, now a professor in the De­ scientist Richard Karp are two of the eight partment of Computer Science and Engineer­ recipients of the highly prestigious National ing at the University of Washington in Seattle, Medal of Science for 1996.The awardees were was cited for his groundbreaking work in theo­ announced by President Clinton in June. retical computer science, carried out while he was a professor at the University of California­ President Clinton cited former Fields Medalist Berkeley. Stephen Smale, professor of mathematics emeritus at the University of California-Ber­ The president described the medal as The Mathematical keley, for four decades of pioneering work on "America's version of the Nobel Prize." He Association of America basic research, leading to major advances in said of the science medalists, "Our nation is 1529 Eighteenth Street, NW pure and applied mathematics. grateful to these visionaries for advancing our Washington, DC 20036 base of knowledge." The National Medal of Science, established by The Mathematical Association of America Second class postage paid at Congress and administered by the National 1529 Eighteenth Street, NW Washington, DC and Science Foundation, honors individuals for additional mailing offices Washington, DC 20036-1385 contributions to the present state of knowledge in one of the following fields: physical, bio­ logical, mathematical, engineering, or social and behavioral sciences. The medal has now been awarded to 344 distinguished scientists and engineers. FOCUS August 1996 FOCUS Editorial FOCUS is published by the Mathematical Association of America six times a year: February, April, June, August, October, and The Good, the Bad, December. Editor: KeithJ. Devlin,Saint Mary's College and the Misunderstood of California; devlin@ stmarys-ca.edu Why would a manager in industry hire a mathematics Ph.D? Associate Editor: Donald J. Albers, MAA Some possible reasons are Associate Executive Director and Director of Publications and Electronic Services; • Mathematicians have highly developed skills in abstraction, analysis of underlying [email protected] structures, and logical thinking. Managing Editor: Harry Waldman, • Mathematicians have expertise with the best tools for formulating and solving prob­ MAA;[email protected] lems. Production Specialist: Amy Fabbri, • Powerful-s-even pure-mathematicians are better equipped to keep going when text­ MAA; [email protected] books have to be left behind. Copy Editor: Nancy Wilson, Saint Mary's College of California; nwilson@stmarys­ • Mathematicians do not always know the answers, but they know the right questions to ca.edu ask and they know when the questions being asked are wrong. Letters to the editor should be addressed to • Mathematicians are better equipped than others in coming up with the correct defini­ Keith Devlin, Saint Mary's College of tions of problems and developing the right level of abstraction. California, P.O. Box 3517, Moraga, CA 94575; [email protected]. • Mathematicians have an ability to deal with abstraction, uncoupled from specific technology and involving many subsystems; to develop models for the abstract sys­ Subscription and membership questions tems; to use a common language (mathematics) to communicate the results; and to should be directed to the MAA Customer Service Center, 1-800-331-1622; e-mail: apply well developed skills to spot hidden gaps and identify connections. [email protected]. The above pluses are all taken from the recent SIAM report Mathematics in Industry. Of The FOCUS subscription price to individual course they are not so much directed at mathematics Ph.D.s as mathematicians in gen­ membersoftheAssociationis$6.00,included eral. Though some of the managers polled for the SIAM report acknowledge that a Ph.D. in the annual dues. (Annual dues for regular can bring a deeper understanding of how to solve difficult problems, the intense focus members, exclusive of annual subscription (and associated acculturation) of a Ph.D. program can lead to problems when the Ph.D. prices for MAAjournals, are $68.00. Student moves from academia to industry-a career path that has become far more common of and unemployed members receive a 66 percent discount; emeritus members receive late than in the days when the Ph.D.'s advisor was a student. Here are some of the a 50 percent discount; new members receive negatives expressed in the report. a 40 percent discount for the first two • A weakness of a mathematician is tunnel vision: write a paper and that's the solution. membership years.) • Mathematicians in general have a bad image; they don't care about the real environ­ Copyright © 1996 by the Mathematical Association of America (Incorporated). ment-realistic models, cost, implementation. They are concerned instead with prov­ Educational institutions may reproduce ing irrelevant theorems. articles for their own use, but not for sale, • It provided that the following citation is used: is important for mathematicians to learn that they can't continue their investigations "Reprinted with permission of FOCUS, the forever. They have to learn to say "enough" in the available time. newsletter of the Mathematical Association The highly narrow focus that is required for most mathematics Ph.D. students to com­ of America (Incorporated)." plete their Ph.D. is clearly not designed to meet the needs reflected in this second set of Second class postage paid at Washington, comments. Nevertheless, every year some mathematics Ph.D.s do transfer successfully DC and additional mailing offices. from academia to industry. What is the magic ingredient that makes this happen? The Postmaster: Send address changes to the SIAM report answers this question as well. To succeed in industry, the mathematics MAA, P.O. Box 90973, Washington, DC 20090-0973; e-mail: [email protected], or Ph.D. needs: call1-800-331-1622(U.S. and Canada only); • good interpersonal skills (301) 617-7800 (outside U.S. and Canada). For advertising information, contact Joseph • good communication skills; in particular being able to explain something to others Watson, MAA, 1529 Eighteenth Street NW, outside the field Washington, DC 20036; (202) 387-5200; e­ mail: jwatson@ maa.org. • breadth of knowledge of other areas ISSN: 0731-2040 • understanding of and interest in practical applications Printed in the United States of America. • willingness to follow up on the problem 2 August 1996 FOCUS Winners of the twenty-fifth USA Math­ setts USAMO ematical Olympiadwere honored at a U.S. and a mem­ Alexander H. Saltman, Austin, Texas Department ofState reception and dinner ber of the on Monday, June 3, hosted by Dr. John H. Daniel A. Stronger, Brooklyn, New York first USA Gibbons, assistant to the president for sci­ team in the The activities began at a sponsoring orga­ ence and technology policy. Members of Interna­ nizations' reception on Sunday at the the mathematical sciences community, the tional Dolciani Mathematical Center where rep­ federal government, and private industry Mathemati­ resentatives of the nine sponsoring societ­ joined to recognize these young individu­ cal Olym- ies of the American Mathematics als' extraordinary achievement. Competitions presented the winners with piad. The Doris Schattschneider; Moravian win n e r s College. The winners are: tokens of appreciation and congratula­ and guests tions. The remarks of Dr. Gail Burrill, Carl 1. Bosley, Topeka, Kansas were then treated to the USAMOAddress, presidentof the National Council ofTeach­ "Some geometric challenges," by Dr. Christopher C. Chang, Palo Alto Califor­ ers ofMathematics, were particularly poi­ Doris Schattschneider of Moravian Col­ nia gnant as she pointed out that it was students lege. like these that had helped to make her Nathan G. Curtis, Reston Virginia teaching career rewarding and challeng­ The reception and dinner, attended by Michael R. Korn, Vadnais Heights, Min­ ing. nearly 140 members of the mathematical nesota community, followed in the Diplomatic On Monday morning, the winners, their Reception Rooms ofthe U.S. Department Carl Miller, Bethesda, Maryland parents, and members of the mathemati­ of State. Dr. Gibbons gave a warm and cal community were invited to attend a Josh Nichols-Barrer, Newton, Massachu- inspiring pre-dinner address wishing the series of lively and interactive lectures awardees well in their personal goals, and by Dr. Sid Graham and other National collectively, in the attemptto win first place Science Foundation mathematicians.