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.

Politicians, real-estate agents, used-car salesmen, and advertising copy-writers are expected to stretch facts in self-serving directions, but scientists who falsify their results are regarded by their peers as committing an inexcusable crime. Yet the sad fact is that the history of science swarms with cases of outright fakery and instances of scientists who unconsciously distorted their work by seeing it through lenses of passionately held beliefs.

The computers are not replacing mathematicians; they are breeding them.

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.

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

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?