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

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

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.

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.

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.

Mathematics is not only real, but it is the only reality. That is that entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure.

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.