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

If God creates a world of particles and waves, dancing in obedience to mathematical and physical laws, who are we to say that he cannot make use of those laws to cover the surface of a small planet with living creatures?

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.

Wouldn't the sentence 'I want to put a hyphen between the words Fish and And and And and Chips in my Fish-and-Chips sign' have been clearer if quotation marks had been placed before Fish, and between Fish and and, and and and And, and And and and, and and and And, and And and and, and and and Chips, as well as after Chips?

Mathematics is not only real, but it is the only reality.

As Bertrand Russell once wrote, two plus two is four even in the interior of the sun.

If you ask me to tell you anything about the nature of what lies beyond the phaneron… my answer is “How should I know?”… I am not dismayed by ultimate mysteries… I can no more grasp what is behind such questions as my cat can understand what is behind the clatter I make while I type this paragraph.

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.

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.

Consider a cow. A cow doesn't have the problem-solving skill of a chimpanzee, which has discovered how to get termites out of the ground by putting a stick into a hole. Evolution has developed the brain's ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.

A god whose creation is so imperfect that he must be continually adjusting it to make it work properly seems to me a god of relatively low order, hardly worthy of any worship.

The universe is almost like a huge magic trick and scientists are trying to figure out how it does what it does.

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

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.

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.

[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.

Let the Bible be the Bible. It's not about science. It's not accurate history. It is a grab bag of religious fantasies written by many authors. Some of its myths, like the Star of Bethlehem, are very beautiful. Others are dull and ugly. Some express lofty ideals, such as the parables of Jesus. Others are morally disgusting.

If present trends continue, our country may soon find itself far behind many other nations in both science and technology nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks.

Mathemagical mathematics combines the beauty of mathematical structure with the entertainment value of a trick.

One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers.

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. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity.

Although Lewis Carroll thought of The Hunting of the Snark as a nonsense ballad for children, it is hard to imagine - in fact one shudders to imagine - a child of today reading and enjoying it.

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

Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all...

Debunking bad science should be constant obligation of the science community, even if it takes time away from serious research or seems to be a losing battle. One takes comfort from the fact there is no Gresham's laws in science. In the long run, good science drives out bad.

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