President Donal O’Shea of New College of Florida is a co-winner of the 2016 American Mathematical Society’s Leroy P. Steele Award for Exposition, one of the highest distinctions in mathematics.
O’Shea and fellow mathematicians David Cox and John Little received the award for their 1992 book Ideals, Varieties and Algorithms. Its fourth edition was released this year.
“We are deeply honored to have been awarded the Steele prize,” O’Shea said. “Many wonderful books and papers in mathematics have appeared in the last few decades, and those singled out by the Steele prize are among the best. Having our book listed in this company is deeply touching.”
The book, nicknamed CLO for its authors’ initials, is known as a classic for making the complex field of algebraic geometry widely accessible.
“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 move computational algebraic and algebraic geometry into the mathematical mainstream, the Society said. “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.”
The Society noted that the three authors of the landmark book are top-flight mathematicians who teach at small liberal arts colleges: O’Shea taught at Mount Holyoke College for more than 30 years before becoming the president of New College in 2012, while Cox teaches at Amherst College and Little teaches at College of the Holy Cross.
“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,” the Society said.
Algebraic geometry has a reputation for being impenetrably technical and abstract. But by requiring only linear algebra as a prerequisite, the society said, CLO has invited a broad audience of readers into a central branch of mathematics.
Using geometry to introduce core topics and appealing to computational theory to prove fundamental results, the authors 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, the Society said.
“Ideals, Varieties and Algorithms was chosen for the Steele Prize because it is a rare book that does it all. It is accessible to undergraduates,” the award citation states. “It has been a source of inspiration for thousands of students of all levels and backgrounds.”
In their response to the Society, the authors wrote:
We are deeply honored and grateful to receive the Leroy P. Steele prize for our book Ideals, Varieties and Algorithms. We started writing it in 1988, partly to provide background materials and notes for students involved in undergraduate research, and partly to provide alternatives to the usual algebra courses for undergraduate mathematics majors.
At that time, new algorithms and ever-faster computing speeds were making it possible for undergraduates to explore examples that would previously have been inaccessible without deeper theoretical tools, a trend which has only increased in the intervening years. Through four editions, we have learned a tremendous amount by working on this project, and our readers include many individuals who expanded our horizons and whom we would never have encountered otherwise.
Many wonderful books and papers in mathematics have appeared in the last few decades, and those singled out by the Steele prize are among the best. Having our book listed in this company gives us great pleasure, and we are deeply touched by the citation.
O’Shea has been recognized previously for his ability to turn complicated mathematical concepts into broadly understandable prose. In 2008, he received the Peano Prize, one of Europe’s top awards for mathematical writing, for his book The Poincaré Conjecture: In Search of the Shape of the Universe (Walker & Company, 2006).
The AMS Steele Prize will be awarded on Thursday, January 7, 2016, at the Joint Mathematics Meetings in Seattle.