All mathematicians share... a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.

One day, when I was doing well in class and had finished my lessons, I was sitting there trying to analyze the game of tic-tac-toe... The teacher came along and snatched my papers on which I had been doodling... She did not realize that analyzing tic-tac-toe can lead into dozens of non-trivial mathematical questions.

Biographical history, as taught in our public schools, is still largely a history of boneheads; ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant general the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician.

A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?

Modern science should indeed arouse in all of us a humility before the immensity of the unexplored and a tolerance for crazy hypotheses.

Speaking about symmetry, look out our window, and you may see a cardinal attacking its reflection in the window. The cardinal is the only bird we have who often does this. If it has a nest nearby, the cardinal thinks there is another cardinal trying to invade its territory. It never realizes it is attacking its own reflection. Cardinals don't know much about mirror symmetry!