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Where's the Fun Stuff?

A student asked, "Where's the fun stuff?", the interesting background and applications that are often omitted from formal course work for lack of time. The most honest answer is, "I don't know," because what one person finds interesting can be boring and trivial to another. What follows is my personal list of "fun stuff", i.e., books that I read and enjoyed as a math student, that helped me make historical connections, know a little about the lives of famous mathematicians, appreciate their achievements, and simply be entertained by stories, jokes, riddles and quotations. That this list consists of books, and mostly rather hoary ones at that, just shows my age. The visitor to this page is encouraged to look among the more recent books of math for the general reader, the growing number of journals and articles for math students and teachers, and the explosion of mathematical web sites, to find his or her own "fun stuff". I hope my colleagues will feel free to make their own lists, to help guide the visitor among the many sources that are available.

Lantz's List of Fun Math Stuff:

• Howard Eves, An Introduction to the History of Mathematics. It is a great help in gaining an overview of mathematics to have some sense of who did what, where, and under what circumstances. Some history of math texts are very thorough in listing contributors and their contributions in technical terms but do not explain those terms (which in some cases have fallen out of use, so they cannot be found elsewhere, either). Eves' text, now in at least its seventh edition, strives for more clarity. I particularly enjoy the "problem studies" at the end of each chapter, where the reader gets to reproduce some of the mathematical achievements of the past, sometimes in its own terms, sometimes using modern methods. Two books that can supplement this text are:
• Eric Temple Bell, Men of Mathematics. The prejudices of the author (and his time) are evident in the title, and he is often accused of not letting the facts get in the way of a good story. But this book of short biographies of great mathematicians of the past lets the reader see them not as just names in a text but people with gifts and flaws.
• Ronald Calinger, ed., Classics of Mathematics. Historical overview, extended excerpts of the (translated) actual articles written by the masters, and biographical and mathematical sketches.
• Edwin A. Abbott, Flatland. Not really a math book; rather a parable for tolerance. But every math person should read this (and its modern extension, Sphereland, and G. H. Hardy's A Mathematician's Apology, and . . . but this one is the place to start).
• Philip J. Davis and Reuben Hersh, The Mathematical Experience. An entertaining description of what being a working mathematician is like. Pure math gets a gentle slap, because the authors are applied mathematicians, but most of it sounds right to me.
• George E. Martin, The Foundations of Geometry and the Non-Euclidean Plane. As a geometry text, there is much to like and much to dislike about this book; the description of non-Euclidean geometry is exceedingly technical. But the "graffiti" at the end of most chapters, mostly quotations from mathematicians and nonmathematicians, are very entertaining and illuminating.
• Underwood Dudley, Mathematical Cranks. A collection of topics about people who may be right (e.g., the Duodecimal Society, who advocate switching to base-12 notation), wrong (the circle-squarers, who try to solve a problem that was long ago proved impossible), or just plain incomprehensible (I've received papers from a few of these myself); but all destined for mathematical oblivion. Dudley has other books (e.g., The Trisectors) and is always clear and fun.
• Petr Beckmann, A History of Pi. This is exactly what the title suggests: A study of the number pi, from ancient approximations (3, in the Old Testament) to modern attempts to set its value by action of the Indiana State Senate. Geometry, calculus, infinite series, etc., all get in there somewhere. It's a chance to see a broad stretch of math from an apparently small starting point.
• Howard Eves, In Mathematical Circles. Quotations and anecdotes about famous mathematicians. Eves just wanted to share a few "goodies" that he had collected with math teachers, to use to jazz up their lectures; but the original two volumes were so popular that he had to add three more. The fourth is Mathematical Circles Adieu, and the fifth, published eleven years later, is Return to Mathematical Circles -- his public demanded more.
• Life Science Library, Mathematics. This is largely a picture book, with elementary introductions to several fields of mathematics; but the pictures are so clear and so colorful that that it's fun to look through (and use as a source for lectures, if needed). The full-page photo of Kurt Gödel is impressive.
• Clifton Fadiman, Fantasia Mathematica. This is largely nonsense with a mathematical slant: Stories about a topology professor who folds himself into a no-sided figure and disappears, and about a house that collapses into a four-dimensional cube; jokes; limericks; and at least one tragic tale by H. G. Wells. It's great fun. There is also a companion volume, The Mathematical Magpie.

There are lots of other books that should be here -- I feel particularly bad about omitting Ross Honsberger's growing number of contributions to the Dolciani Mathematical Expositions series, and Ivars Peterson's Islands of Truth and The Mathematical Tourist -- but I came to them late, and I intended this list to be the ones I've known and enjoyed for a long time. I hope you enjoy them, too!

email: dlantz@mail.colgate.edu
phone: 315-228-7737
fax: 315-228-7004