Harmony of the World

Who would expect to find in the pages of Mathematics Magazine the first full treatment of one of the more important and oft-cited twentieth-century theorems in analysis, the Stone-Weierstrass Theorem in an article by Marshall Stone himself? Where else would one look for proofs of trigonometric identities using commutative ring theory? Or one of the earliest and best expository articles on the then new Jones knot polynomials, an article that won the prestigious Chauvenet Prize? Or an amusing article purporting to show that the value of pi has been time dependent over the years? These and much more are in this collection of the best from Mathematics Magazine. Readers are inundated with new material in the many mathematical journals. Gems from past issues of Mathematics Magazine or the Monthly or the College Mathematics Journal are read with pleasure when they appear, but get pushed into the background when the next issues arrive. So from time to time it is rewarding to go back and see just what marvelous material has been published over many years, articles now to some extent forgotten. There is history of mathematics (algebraic numbers, inequalities, probability and the Lebesgue integral, quaternions, Polya's enumeration theorem, and group theory) and stories of mathematicians (Hypatia, Gauss, E. T. Bell, Hamilton, and Euler). The list of authors is star-studded: E. T. Bell, Otto Neugebauer, D. H. Lehmer, Morris Kline, Einar Hille, Richard Bellman, Judith Grabiner, Paul Erdos, B. L. van der Waerden, Paul R. Halmos, Doris Schattschneider, J. J. Burckhardt, Branko Grunbaum, and many more.