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

[T]he more the public is confused, the easier it falls prey to doctrines of pseudo-science which may at some future date recieve the backing of politically powerful groups [...]a renaissance of German quasi-science paralleled the rise of Hitler.

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.

The violence and double-talk in the Alice books probably does no harm to children, but the novels should not be allowed to circulate indiscriminately among adults who are undergoing analysis.

The sudden hunch, the creative leap of mind that "sees" in a flash how to solve a problem in a simple way, is something quite different from general intelligence.

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!

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.