The Story of Ideals, Varieties and Algorithms

Late in 2015 the three of us received an email from the American Mathematical Society notifying us that we had won the Leroy P. Steele Prize for Mathematical Exposition for our text Ideals, Varieties and Algorithms, published in 1992 and now in its fourth edition [4]. We were stunned. True, many readers over the years have told us that they loved the book. Nonetheless, the book was written for undergraduates, and to our knowledge no book written explicitly for undergraduates had ever won the Steele Prize. We are often asked how the book got started, and we individually answer as best we can. When the Notices asked, we decided to pool our memories and offer the following account.With the advantage of over twodecades of hindsight, we realize how much we owe to accident.