Contributors

Kathleen Ambruso Acker received her doctorate in mathematics education from American University and works as an independent researcher in mathematics education. Her research interests include teaching with technology, teaching students with learning disabilities, mathematics education as it applies to home-schooled students, and the history of mathematics. Presently she works for American University teaching graduate students enrolled in the Teach for America program.

David L. Alderson is assistant professor of operations research at the Naval Postgraduate School, Monterey, California. Information on his work can be found on his Web site, http://faculty.nps.edu/dlalders/.

Samuel Arbesman is a postdoctoral research fellow in the Department of Health Care Policy at Harvard Medical School and is affiliated with the Institute for Quantitative Social Science at Harvard University. He is a regular contributor to the Ideas section of the Boston Globe.

Philip L. Bowers is professor and chair of the Mathematics Department at Florida State University, where he has taught and nurtured his passion for mathematics for over twenty-five years. Aside from his research interest in geometry and topology, he has a keen appreciation of the historical and philosophical aspects of the subject, as well as an enduring interest in both the technical and philosophical aspects of modern theoretical physics.

Carlo Cellucci is professor of logic at the University of Rome–La Sapienza. He is the author of four books, Teoria della dimostrazione (Proof Theory, 1978), Le ragioni della logica (The Reasons of Logic, 1998), Filosofia e matematica (Philosophy and Mathematics, 2002), and Perché ancora la filosofia (Why Still Philosophy, 2008). He is currently completing another book, Remaking Logic: What Is Logic, Really?

Barry A. Cipra is a freelance mathematics writer based in Northfield, Minnesota. He has been a contributing correspondent for Science magazine and a regular writer for SIAM News, the monthly newsletter of the Society for Industrial and Applied Mathematics. He is the author of Misteaks . . . and How to Find Them Before the Teacher Does: A Calculus Supplement, published by A.K. Peters, Ltd.

Mark Colyvan is professor of philosophy and director of the Sydney Centre for the Foundations of Science at the University of Sydney, Australia. He is the author of The Indispensability of Mathematics (Oxford University Press, 2001), co-author (with Lev Ginzburg) of Ecological Orbits: How Planets Move and Populations Grow (Oxford University Press, 2004), and author of a number of articles in and around the philosophy of mathematics, logic, formal decision theory, and their applications.

Chandler Davis, though he failed in 1992 to stop the University of Toronto from making him emeritus, remains a mathematician and editor—recently, co-editor—of The Mathematical Intelligencer. For some of his nonmathematical prose, see It Walks in Beauty, edited by J. Lukin (Aqueduct, 2010).

Philip J. Davis holds a doctoral degree from Harvard University and is currently professor emeritus in the Division of Applied Mathematics at Brown University. He is known for his work in numerical analysis and approximation theory, as well as his investigations and writings on the history and philosophy of mathematics.

Keith Devlin is a mathematician at Stanford University. He is a Fellow of the American Association for the Advancement of Science. He has written twenty-eight books and published more than eighty research articles. The recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award, he is also “the Math Guy” on National Public Radio.

Alicia Dickenstein is professor of mathematics in the School of Exact and Natural Sciences of the University of Buenos Aires and a principal researcher of the Scientific Research Council of Argentina (CONICET). She has been an invited visiting professor and guest scientist at many institutions throughout the world. Dickenstein is currently working in the area of algebraic geometry and its applications, a subject on which she has co-organized several international conferences. Her publications include not only numerous research articles in prestigious journals and chapters in books on her specialty, but also textbooks on mathematics for children ages nine through twelve.

John C. Doyle is the John G. Braun Professor of Control & Dynamical Systems, Electrical Engineering, and BioEngineering at Caltech, Pasadena, California. Information on his work can be found on his Web site, http:// www.cds.caltech.edu/~doyle/.

Freeman Dyson is a retired professor at the Institute for Advanced Study in Princeton, New Jersey. He began his career as a pure mathematician in England but switched to physics after moving to the United States. A volume of his selected papers in mathematics and physics was published by the American Mathematical Society in 1996.

Harold M. Edwards is professor emeritus of mathematics at New York University. He has received the Whiteman and Steele prizes of the American Mathematical Society and is the author of eight books: Advanced Calculus, Riemann’s Zeta Function, Fermat’s Last Theorem, Galois Theory, Divisor Theory, Linear Algebra, Essays in Constructive Mathematics, and Higher Algebra.

Timothy Gowers is a Royal Society 2010 Anniversary Research Professor at the University of Cambridge. He works in analysis and combinatorics. For his work in these areas he was awarded a European Mathematical Society prize in 1996 and a Fields Medal in 1998.

Judith V. Grabiner is the Flora Sanborn Pitzer Professor of Mathematics at Pitzer College, one of the Claremont Colleges in California. She is the author of The Origins of Cauchy’s Rigorous Calculus (MIT Press) and The Calculus as Algebra: J.-L. Lagrange, 1736–1813 (Garland Press), as well as a Teaching Company DVD course titled “Mathematics, Philosophy, and the ‘Real World.’” She has received several Lester Ford and Allendoerfer Awards from the Mathematical Association of America and the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching from the MAA in 2003.

Mary W. Gray is professor and chair of the Department of Mathematics and Statistics at American University, Washington, D.C. She has received the Presidential Award for Excellence in Science, Engineering and Mathematics Mentoring and is a Fellow of the American Statistical Association. A lawyer as well as a statistician, Dr. Gray has over 100 publications in statistics, economic equity, law, and mathematics education.

Branko Grünbaum received a doctoral degree from Hebrew University in Jerusalem in 1957. He is professor emeritus at the University of Washington, where he has taught since 1966. His book, Convex Polytopes (1967, 2003), has been very popular, as was the book Tilings and Patterns (co-authored with G. C. Shephard), published in 1986. He hopes that the volume Configurations of Points and Lines (2009) will revive interest in this exciting topic, which was neglected during most of the twentieth century. Grünbaum’s interests are mostly in various branches of combinatorial geometry. He has been a Guggenheim Fellow and a Fellow of the AAAS. The American Mathematical Society awarded him a Leroy P. Steele prize, and the Mathematical Association of America awarded him the Lester Ford and Carl Allendoerfer prizes.

Brian Hayes is senior writer for American Scientist magazine and a former editor of both American Scientist and Scientific American. He is also the author of Infrastructure: A Field Guide to the Industrial Landscape (W. W. Norton, 2005) and Group Theory in the Bedroom and Other Mathematical Diversions (Hill and Wang, 2008). He has been journalist-in-residence at the Mathematical Sciences Research Institute in Berkeley and a visiting scientist at the Abdus Salam International Centre for Theoretical Physics in Trieste. He is the winner of a National Magazine Award.

Orit Hazzan is associate professor in the Department of Education in Technology and Science of the Technion–Israel Institute of Technology. In her current research on computer science and software engineering education she partially relies on her research background in mathematics education. In addition to about 100 papers Hazzan has published in refereed journals and conference proceedings, she is also a co-author of two books: Human Aspects of Software Engineering (Charles River Media, 2004) and Agile Software Engineering (Springer, 2008).

Theodore P. Hill is professor emeritus of mathematics at Georgia Tech and has held visiting appointments in Costa Rica, Germany (Gauss Professor), Holland (NSF-NATO Fellow), Israel, Italy, and Mexico. He studied at West Point (BS), Stanford (MS), Göttingen (Fulbright Scholar), and the University of California–Berkeley (MA, PhD). His primary research interests are in mathematical probability, especially optimal-stopping theory, fair-division problems, and Benford’s law.

Howard T. Iseri is professor of mathematics at Mansfield University of Pennsylvania. In mathematics, he likes to find ways to make geometric concepts accessible and intuitive. Outside of math, he is obsessed with the idea that his bikes, feet, and kayaks are too slow.

Vijay Iyer is a pianist, composer, bandleader, and producer in New York City. His fourteen albums include Historicity, winner of the Village Voice and Downbeat Magazine critics’ polls and Germany’s Echo Award. In addition to his work in jazz, Iyer has composed orchestral and chamber works; scored for film, theater, radio, and television; collaborated with poets and choreographers; and joined forces with artists in hip-hop, rock, experimental, electronic, and Indian classical music. He teaches at New York University and the New School. His writings appear in Music Perception, Journal of Consciousness Studies, Current Musicology, Critical Studies in Improvisation, Jazz-Times, Wire, The Guardian, and the anthologies Uptown Conversation, Sound Unbound, and Arcana IV.

Behzad Jalali is director of educational services in the Department of Mathematics and Statistics of the American University, Washington, D.C. His research focus is on teaching mathematics to students with disabilities, as well as on the role of language in mathematics learning.

Tim Johnson is the UK Research Council’s Academic Fellow in Financial Mathematics at Heriot-Watt University and the Maxwell Institute for Mathematical Sciences in Edinburgh, Scotland. He studied physics as an undergraduate, then worked in the oil industry, where he realized guessing was not a good policy when uncertainty and money are involved, and so became a mathematician. His research is centered on the field of stochastic optimal control.

Ann Kajander is associate professor of mathematics education at Lakehead University, Thunder Bay, Ontario, Canada. She has taught mathematics at both the secondary and post-secondary levels and has received a teaching award from Lakehead University. She has published two books for teachers, the more recent being Big Ideas for Growing Mathematicians.

Erica Klarreich is a mathematics and science writer based in Berkeley, California. She holds a doctorate in mathematics from Stony Brook University and a certificate in science writing from the University of California, Santa Cruz. Her articles have appeared in Nature, New Scientist, American Scientist, Science News, and other publications.

Uri Leron is emeritus holder of the Churchill Family Chair of Education in Science and Technology at the Technion–Israel Institute of Technology. He was a ring theorist before switching his research interests to mathematical thinking and learning. He was awarded a residency at the Rockefeller Center in Bellagio, Italy, to study the implications of cognitive psychology and evolutionary psychology for mathematical thinking in general, and for understanding the sources of ubiquitous and recurring errors in particular.

Miroslav Lovric is a professor in the Department of Mathematics and Statistics at McMaster University, Hamilton, Ontario. His areas of research interest include differential geometry, applied mathematics and mathematics education. Besides publishing his research, Lovric wrote a textbook on vector calculus, and is currently working on a textbook for life sciences mathematics. In 2001 Lovric was awarded the national 3M teaching award.

Melvyn B. Nathanson is professor of mathematics at the City University of New York (Lehman College and the Graduate Center) and the author of more than 150 research papers and books in mathematics. Before becoming a mathematician he was an undergraduate major in philosophy at the University of Pennsylvania and a graduate student in biophysics at Harvard University.

Michael Nielsen is a Toronto-based writer currently completing a book titled Reinventing Discovery, about the use of collective intelligence in science. He was formerly a theoretical physicist and is co-author of the standard text in quantum computing.

Nick Paumgarten has been a staff writer for the New Yorker since 2005. From 2000 to 2005 he was the deputy editor of The Talk of the Town, to which he regularly contributes. He has also written features on subjects ranging from sports talk radio to backcountry skiing. Before coming to the New Yorker, Paumgarten was a reporter and senior editor at the New York Observer. Paumgarten lives in Manhattan.

Andrzej Pelc received a doctorate in mathematics in 1981 from the University of Warsaw, Poland. He is currently professor of computer science and director of the Research Chair in Distributed Computing at the Université du Québec en Outaouais, Gatineau, Quebec, Canada. He has published more than 250 papers in computer science and mathematics. Pelc is the recipient of the 2003 Prize for Excellence in Research from the Université du Québec en Outaouais.

David Pimm has been a professor of mathematics education since 2003 at the University of Alberta, Canada. Much of his academic career prior to 2003 was spent at the Open University in the United Kingdom, in the Faculty of Mathematics. He is the author of two books, Speaking Mathematically and Symbols and Meaning in School Mathematics, and editor or co-editor of seven others, including most recently Mathematics and the Aesthetic: New Approaches to an Ancient Affinity (Springer, 2006), with Nathalie Sinclair and William Higginson, in the CMS series.

Julie Rehmeyer is a math and science writer in Berkeley, California. She did graduate work in mathematics at MIT and taught math and the classics at St. John’s College. She has written for Science News, Wired, Discover, New Scientist, and many other publications.

Nathalie Sinclair is associate professor at Simon Fraser University in the Faculty of Education. She co-edited the book Mathematics and the Aesthetic: New Approaches to an Ancient Affinity (Springer) and authored two books related to school mathematics: Mathematics and Beauty: Aesthetic Approaches to Teaching Children (Teachers College Press) and The History of the Geometry Curriculum in the United States (IAP). In addition to her interests in the aesthetic dimension of mathematics and in history, she studies the use of digital technology in mathematics teaching and learning, with a special interest in dynamic geometry software.

Steven Strogatz is the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. In 2007 he received the JPBM Communications Award, a lifetime achievement award for the communication of mathematics to the general public. His books include Sync (Hyperion, 2003) and The Calculus of Friendship (Princeton University Press, 2009).

Robert Thomas is a Fellow of St John’s College and professor in the Department of Mathematics, both at the University of Manitoba, Winnipeg, Canada. He teaches mathematics, chiefly to engineering students; does mathematical research; and edits Philosophia Mathematica, the journal on the philosophy of mathematics published by Oxford Journals. His article title is due to Chandler Davis.

William P. Thurston is professor of mathematics and computer science at Cornell University. He is a pioneer in the field of low-dimensional topology. For the depth and originality of his contributions to mathematics he was awarded the Fields Medal in 1982.

David Wagner is associate professor in the Faculty of Education at the University of New Brunswick. His research focuses on human interactions in mathematics and mathematics learning situations, and how these interactions are structured in speaking and writing in these environments.

Anne Watson is professor of mathematics education at the University of Oxford, where she has worked in teacher education since 1996. Before that she was a secondary mathematics teacher in challenging schools, maintaining a lifelong commitment to helping more students achieve in mathematics, summarized in Raising Achievement in Secondary Mathematics (Open University Press).

Walter Willinger is a member of the Information and Software Systems Research Lab at AT&T Labs-Research, Florham Park, New Jersey. Information on his work can be found on his Web site, http://www.research.att.com/people/Willinger_Walter/index.html.

Henryk Woźniakowski is professor of computer science at Columbia University, New York, and professor of applied mathematics at the University of Warsaw, Poland. His main research interest is computational mathematics, in particular the computational complexity of continuous problems.