The Mathematical Association of America (MAA) has named David A. Cox, the William J. Walker of Mathematics at Amherst, one of this year’s winners of its Lester R. Ford Award honoring the author of an outstanding paper published in the previous year. Cox was recognized for his article “Why Eisenstein Proved the Eisenstein Criterion and Why Schönemann Discovered It First,” which appeared in the January 2011 issue of the MAA’s The American Mathematical Monthly, and accepted the award during the MAA Prize Session on Aug. 3 at the 2012 MAA MathFest in Madison, Wisc.
According to Cox, “Why Eisenstein” discusses the historical context of what is called “the Eisenstein Criterion” in the theory of polynomials. Cox explains in the piece that Gotthold Eisenstein, for whom the criterion was named, was not actually the first to discover it; that honor goes to Theodor Schönemann. “The amazing thing is that Eisenstein and Schönemann were led to their discoveries by completely independent paths,” he said. “They really should both get credit.” He also explored some of the related developments in algebra and number theory that were occurring in the 19th century.
In the citation for Cox’s award, the MAA described the Amherst professor’s paper as “an engrossing tale” and “an amazingly rich story, beautifully told, not of a priority dispute but of a grand sweeping flow of ideas beginning with [Carl Friedrich] Gauss (who partially scooped both Schönemann and Eisenstein) and extending into the beating heart of modern-day mathematics. It is a tour de force of mathematical and historical scholarship.”
For Cox, such praise and the honor itself are huge compliments. “I put a high value on quality expository writing in mathematics, so it is very satisfying when my peers recognize my contribution.” What is also gratifying, said Cox, is that the same mathematics that led to his paper also resulted in a senior thesis. “[My paper] mentions Niels Henrik Abel’s wonderful theorem about geometric constructions on a curve called the lemniscate,” he noted. “Eisenstein proved his criterion in the course of trying to understand Abel’s proof. I liked Eisenstein’s argument so much that I included a proof of Abel’s theorem in a book on Galois theory that I wrote in 2004. But my treatment had one loose end –there was one Galois group I couldn't compute. Last September, I gave this problem to Trevor Hyde ’12 for his senior thesis in mathematics. Trevor solved the problem in spectacular fashion—his thesis was awarded summa cum laude, and he received an Amherst College Post-Baccalaureate Research Fellowship.” What’s more, said Cox, he and Hyde will write up his thesis for publication in a mathematical journal.
Cox, a member of the Amherst faculty since 1979, received his bachelor of arts degree from Rice University and Ph.D. from Princeton University. His research interests include algebraic geometry, commutative algebra, geometric modeling, number theory and the history of mathematics.
According to the MAA’s website, the Lester R. Ford Awards were established in 1964 to recognize authors of articles of “expository excellence published in The American Mathematical Monthly or Mathematics Magazine.” Named for mathematician Lester R. Ford, Sr., editor of the American Mathematical Monthly from 1942 to 1946 and president of the Mathematical Association of America from 1947 to 1948, the prize and $500 are given to up to five mathematicians annually at the summer meeting of the MAA.
Cox is not the first member of Amherst’s math department to win a Ford Prize. Dan Velleman, Julian H. Gibbs ’46 Professor of Mathematics, and Tanya Leise, assistant professor of mathematics, received the award in 1994 and 2008, respectively.