MAA Writing Awards
Are There Coincidences in Mathematics?
Year of Award: 1982
Publication Information: The American Mathematical Monthly, vol. 88, 1981, pp. 311-320
Summary: E. H. Moore once wrote, "The existence of analogies between the central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to their central features." This article twists this quote around to discuss whether a "common feature" could be a coincidence which one has observed in several places. Examples from many levels of mathematics are used to temper the discussion.
About the Author: (from The American Mathematical Monthly, vol. 88, (1981)) Philip Davis received his Ph.D. from Harvard under Ralph Boas. He has taught at Harvard, Maryland, the University of Utah, and Brown. He has extensive industrial and government experience, including five years as Chief, Numerical Analysis Section, National Bureau of Standards; he was a Guggenheim Fellow in 1956-57. His extensive work in numerical analysis and applied mathematics includes the books Interpolation and Approximation (1963), Mathematics of Matrices (1964), Numerical Integration (with P. Rabinowitz, 1967), Circulant Matrices (1979). A new book, The Mathematical Experience, written jointly with Professor Reuben Hersh of the University of New Mexico, appeared recently. Professor Davis received the 1960 Award in Mathematics of the Washington Academy of Sciences and the MAA Chauvenet Prize in 1963.