at THE NEWSLETTER OF THE MATHEMATICAL ASSOCIATION OF AMERICA .: 1&1 II :I ::::» z o N 1&1 :I .::::»... o > o o o N III: 1&1 II :Ii .1&1 U 1&1 a INSIDE: Art Inspired hy Mathcmatics in New York ................................................................................ .4 (;conlctry for a New (:entury ..................................................................................................... 1) Ah'lI1doning De.ld Ends: Emhmdng Lively Beginnings .......................................................... J() The Brain in the Box ................................................................................................................. 1J FOCUS DECEMBER 2000 FOCUS IS published by the Mathematical Association of America in January, February, March, April, Mayl)une, August/September, October, November. and a FOCUS December. Editor: Fernando Gouvea. Colby College; [email protected] December 2000 Managing Editor: Carol Baxter. MAA Volume 20, Number 9 [email protected] Senior Writer: Harry Waldman. MAA [email protected] Inside Please address advertising inquiries to: Kate 4 Art Inspired by Mathematics in New York Debelack. MAA; [email protected] By Ivars Peterson President: Thomas F. Banchoff. Brown University 6 Science and Technology Policy Site Now Part of MAA Online First Vice-President: Barbara L. Osofsky. By Al Buccino Second Vice-President: Frank Morgan. Secretary: Martha J. Siegel. Associate Secretary: James J. Tattersall. Treasurer: 8 MAA Issues Revised Guidelines for Undergraduate Gerald J. Porter Programs and Departments Executive Director: Tina H. Straley By John Fulton Associate Executive Director and Director of Publications and Electronic Services: 9 Geometry for a New Century Donald J. Albers By Joseph Malkevitch FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin 10 Abandoning Dead Ends: Embracing Lively Beginnings Colligan; Ed Dubinsky; Bill Hawkins; Dan By Edward B. Burger and Michael Starbird Kalman; Maeve McCarthy; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 12 Thinker Mills: Letters to the editor should be addressed to A Contradiction in Terms for Universities in an Age of Automation Fernando Gouvea. Colby College, Dept. of Mathematics, Waterville, ME 04901. By Brian A. Hagler Subscription and membership questions should be directed to the MAA Customer 13 A Different Pencil: The Brain in the Box Service Center, 800-331-1622; e-mail: By Frank C. Wilson [email protected]; (301) 617-7800 (outside U.S. and Canada); fax: (301) 206-9789. 14 Short Takes Copyright © 2000 by the Mathematical Association of America (Incorporated). 15 Dirk Jan Struik: Mathematician, Historian, and Marxist Educational institutions may reproduce By Arthur B. Powell and Marilyn Frankenstein articles for their own use. but not for sale. provided that the following citation is used: "Reprinted with permission of FOCUS. the 18 Employment Opportunities newsletter of the Mathematical Association of America (Incorporated)." On the cover: "Quartic" by Clifford Singer. Acrylic on Plexiglas, 30 by 30 inches. ( 1999.) Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. Box 90973. Washington, DC 20090-0973. FOCUS Deadlines ISSN: 0731-2040; Printed in the United States February March April of America. Editorial Copy December 15 January 19 Display Ads January 4 February 4 February 22 Employment Ads December 19 January 26 February 15 2 DECEMBER 2000 FOCUS AAAS Meeting to Offer Strong Mathematics Program T he 2001 Annual Meeting of the The Role of Mathematics in Pricing and tober 20th, 2000 issue of Science or visit American Association for the Advance­ Hedging Financial Assets (Philip Protter) the AAAS Annual Meeting web site at ment of Science will be held on February http://www.aaas.org/meetings. 15-20, in San Francisco, CA. As usual, the The Mathematics of Congressional and meeting will feature many outstanding Other Apportionments (Donald G. Saari) AAAS annual meetings are intended to expository talks by prominent mathema­ be showcases of American science, but ticians. These include the following three­ Other symposia that will be of interest to participation by mathematicians and hour symposia sponsored by Section A the mathematical community include: mathematics educators is often lower (Mathematics) of the AAAS: From Juggling and Magic to Combinato­ than might be expected. AAAS program rics, Understanding Music with Statistical committees are usually very interested in Beauty and the Beast: Realizations of the Methods, Designing, Implementing, and offering symposia on mathematical top­ Art in Mathematics (Michael Field) Assessing Active Learning College Science ics. Thus, Section lfs Committee is seek­ and Mathematics, Mathematical Statistics ing organizers and speakers who can Mathematics of the Visual Cortex (Jack in Natural Language Analysis, Mathemati­ present substantial new material in an Cowan) cal and Computational Properties of Uni­ accessible manner to a large scientific versal Grammar Under Optimality Theory, audience. The Section would also like to The Nature and Origins of Mathematical The Sea of Data and How to Manage It, invite mathematicians to attend the Sec­ Thinking (Keith Devlin) Science and Mathematics Education: Cali­ tion A Committee business meeting 7:30- fornia Since the End ofAffirmativeAction, 10:30 P.M. Friday, February 16th, 2001 in Mathematical Aspects ofIntellectual Prop­ and Journey Beyond TIMSS; Rethinking Mason room B of the San Francisco erty Management on the Internet (Mat­ Professional Development. These are, of Hilton. Warren Page, the Secretary of Sec­ thew Franklin) course, only a few of the 150 or so AAAS tion A, is looking for proposals for sym­ program offerings in the physical, life, posia for future AAAS annual meetings. Applications of Mathematics to Problems social, and biological sciences. For details He can be reached by email at in Medicine (Parros M. Pardalos) of the 2001 AAAS program, see the Oc- [email protected] .• 2001 Tensor Grants: Call For Proposals for Women and Mathematics Projects T he MAA plans to award grants for ematics faculty to develop projects to in­ Proposals should be submitted as soon projects designed to encourage college crease participation of women in math­ as possible but must arrive no later than and university women or high school and ematics, and provide support to project February 5, 2001. The MAA/Tensor middle school girls to study mathemat­ directors. Foundation intends to make ten grants. ics. The Tensor Foundation, working Please do not hesitate to contact the Pro­ through the MAA, is soliciting college, Grants of up to $5,000 will be made to gram Director, Dr. Florence Fasanelli, university and secondary mathematics the institution of the project director to (202-966-5591 or [email protected]) faculty (in conjunction with college or be spent within the year. An institution for assistance in preparing your proposal. university faculty) and their departments is expected to supply matching funds or and institutions to submit proposals. in-kind support as an indication of Complete guidelines are posted on MAA Projects may replicate existing successful commitment to the project. Grants will Online at http://www.maa.org/projects/ projects, adapt components of such be made to college and university math­ solic_99.html. Please review the guide­ projects, or be innovative. ematics faculty or secondary school or lines before submitting proposals. • middle school mathematics faculty work­ The objectives of the MAAlTensor Foun­ ing in conjunction with college or uni­ dation Program are to encourage math- versity faculty. 3 FOCUS DECEMBER 2000 Art Inspired by Mathematics in New York By Ivars Peterson Most people don't expect to encoun­ festations and many others testify to the vent of powered flight to the unveiling of ter mathematics on a visit to an art gal­ creativity inherent in both mathematics the atomic nucleus and Albert Einstein's lery. At first (or even second) glance, art and art. formulation of the special and general and mathematics appear to have very theories of relativity. At the same time, little in common, though both are prod­ More generally, conceived as explorations the development of non-Euclidean ge­ ucts of the human intellect. Looking at of form, space, light, and color, sculptures, ometries, which overturn Euclid's postu­ art with a mathematical eye or at math­ paintings, and other artworks can them­ late that parallel lines never meet, pro­ ematics with an artistic eye, however, can selves embody a variety of mathematical vided alternative but perfectly consistent be illuminating and immensely reward­ principles, expressed not only in such models of reality. Such concepts offered ing. And there is much more to see than obviously geometric objects as triangles, artists avenues of escape from conven­ one would expect. circles, spheres, and cones but also tional representation. Obsessively explor- ing new math­ The Art & Mathemat­ ematical ideas, ics 2000 exhibit at the from fractals to Cooper Union in New chaos, today's York City offers a rich creators continue sampling of artworks that tradition. inspired by math­ ematics, ranging from Examples of the gracefully curved mathematics as sculptures of Brent art and art as Collins and tensegrity mathematics structures of Kenneth abound in all Snelson to the playful sorts of settings­ polyhedra of George indeed, almost Hart and wavy anywhere one painted grids of Doug