One of my greatest pleasures and privileges was writing a column, over
a period of some 30 years, for Scientific American. It began with an
article on hexaflexagons in December 1956 and concluded with a col-
umn on minimal Steiner trees in May 1986.
Writing this column was a marvelous learning experience. I took
no courses in math when I was an undergraduate at the University of
Chicago-my major was philosophy-but I have always loved mathemat-
ics, and now and then regret I did not pursue it as a career. It takes
only a glance through earlier book collections of the columns to see
how they gradually became more sophisticated as I learned more about
mathematics. Not the least of my delights was getting to know many
truly eminent mathematicians who generously contributed material and
who have since become lifelong friends.
This is the fifteenth and final collection. As in previous books in
the series, I have done my best to correct blunders, to expand and
update each column with an addendum, to add new illustrations, and
to provide fuller lists of selectcd references.