Unfortunately, as recent studies of' education in this country
have made clear, one of the chief characteristics of mathemat-.
ical classes, especially on the lo~ver levels of public education, is
ennui. Some teachers may be poorly trained in mathematics
and others not trained at all. If mathematics bores them, can
you blame their students for being bored?
Like science, mathematics is a kind of game that we play ~vith
the universe. The best mathematicians and the best teachers of
mathematics obviously are those who both understand the
rules of the game, and who relish the excitement of playing it.
Raymond Smullyan, who has enormous zest for the games of
philosophy and mathematics, once taught an elementary
course in geometry. In his delightful book 5000 U.C. and 0 t h ~ ~
Philosophical Fantasies (1983) he tells how- he once introduced
his students to the Pythagorean theorem