Content area
Full Text
MATHEMATICS Theorems to Savor James Propp THE ART OF MATHEMATICS: Coffee Time in Memphis. Béla Bollobás. xvi + 359 pp. Cambridge University Press, 2006. $85 doth, $34.99 paper.
The mathematician and puzzle connoisseur Peter Winkler once joked, with a nod to Isaac Newton, "If I have seen farther than others, it is because I have stood on the shoulders of Hungarians." One of these Hungarians is the late Paul Erdos, famous within mathematics for his contributions to number theory and combinatorics and famed more broadly for his unique lifestyle and lingo (children are "epsilons," God is the "Supreme Fascist," God's collection of the best mathematical proofs is "The Book," and so forth). Many of Erdos's collaborators and successors are also Hungarian, and others have adopted what might be called "the Hungarian style," with an emphasis on snappy problems and clever solutions. I can think of no better way to get acquainted with these people and their work than to spend a few months periodically dipping into Béla Bollobás's new collection of mathematical puzzles, titled The Art of Mathematics: Coffee Time in Memphis.
Bollobás (the name is pronounced "bowl o' bosh") is one of the most ardent keepers of the Erdos flame. Since Erdos died-or, as Erdös would say, "left"-in 1996, Bollobás has organized a conference in his honor every year at the University of Memphis. (Full disclosure: I spoke at the 2006 conference.) Bollobás, a professor who divides his time between Trinity College (Cambridge) and the University of Memphis, has worked for decades in functional analysis, combinatorics and graph theory. In the course of years of teaching and research, he has devised (or learned of) many easily stated problems whose solutions possess one or more of the hallmarks that mathematicians prize, such as economy, surprise and fecundity.
Here is one of my favorites: Suppose 10 chairs are arranged in a circle, half of them occupied by students. Show that there exists some whole number n between 1 and 9 such that if each of the 5 students moves n...