Do We Teach Too Much Mathematics . . . ?

For more than five decades, Frank Swetz has advocated for the use of history and culture to enliven and deepen the study of mathematics. In particular, he has described how mathematical developments in non-Western societies might be incorporated into the training of secondary school teachers. His books include Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China (The Penn State Press, 1977), From Five Fingers to Infinity: A Journey Through the History of Mathematics (Open Court Publishing, 1994), and Mathematical Expeditions: Exploring Word Problems Across the Ages (Johns Hopkins University Press, 2012). More information on his career may be found here. As a founding editor of MAA Convergence, he focused especially on soliciting and preparing book reviews and on creating an extensive collection of Mathematical Treasures, visual images of interesting and great books or objects in the history of mathematics for use as illustrations in mathematics classes.

The following essay is something of a valedictory address, exploring what mathematics is and why and how to teach it. It thus highlights 'humanizing mathematics', the value of historical examples, and other major themes of Frank's career.