image: David A. Cox, one of the winners of the 2016 AMS Steele Prize for Exposition view more
Credit: Charles Quigg, Office of Communications, Amherst College
The AMS Leroy P. Steele Prize for Exposition will be awarded to three mathematicians: David Cox (Amherst College), John Little (College of the Holy Cross), and Donal O'Shea (New College of Florida). They are honored "for their book Ideals, Varieties, and Algorithms, which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers in many fields."
Algebraic geometry has a reputation for being impenetrably technical and abstract. By requiring only linear algebra as a prerequisite, the book by Cox, Little, and O'Shea invites a broad audience of readers into this central branch of mathematics. Using geometry to introduce core topics and appealing to computational theory to prove fundamental results, they complement the development of theoretical results with applications to such topics as automated theorem proving and robotics. All of this is delivered with crystal-clear exposition and top-quality writing.
"Even more impressive than [the book's] clarity of exposition is the impact it has had on mathematics," the prize citation states. "CLO, as it is fondly known, has not only introduced many to algebraic geometry, it has actually broadened how the subject could be taught and who could use it." The book helped bring the topic of computational algebra into the mathematical mainstream. In particular, the book's presentation of the theory of Gröbner bases "has done more than any other book to popularize this topic." Gröbner bases provide a way to efficiently automate certain calculations in algebraic geometry (see "What is a Gröbner Basis?", by Bernd Sturmfels, in the November 2005 issue of the Notices of the AMS). The subject of Gröbner bases has boomed in recent years, in part because of significant applications to such diverse problems as oil exploration, software design, genetics, and robot kinematics.
Originally published by Springer Verlag in 1992, the fourth edition of CLO appeared just this year. The book has truly become a classic. It not only has provided many of today's mathematicians with their first grounding in algebraic geometry, but also has brought this area of mathematics to the service of scientists and engineers. All three authors are top-flight mathematicians at small colleges; O'Shea was at Mount Holyoke College for more than 30 years before becoming the president of New College of Florida in 2012. Their book shows how small colleges make signal contributions to the advancement of mathematics, the training of future mathematicians, and the applications of mathematics to other disciplines.
Cox received the Lester R. Ford Prize from the Mathematical Association of America (2012) and was elected as a Fellow of AMS (2013). Little has received distinctions for his outstanding service to the College of the Holy Cross, including its Distinguished Teaching Award (2003) and the Anthony and Renee Marlon Professorship in the Sciences (2012-2015). In 2008, O'Shea received the Peano Prize for his book The Poincaré Conjecture: In Search of the Shape of the Universe (Walker & Company, 2006).
Presented annually, the AMS Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded on Thursday, January 7, 2016, at the Joint Mathematics Meetings in Seattle.
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Find out more about AMS prizes and awards at http://ams.org/prizes-awards/prizes.
Founded in 1888 to further mathematical research and scholarship, today the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.