There are gaps in the fossil graveyard, places where there should be intermediate forms, but where there is nothing whatsoever instead. No paleontologist..denies that this is so. It is simply a fact, Darwin's theory and the fossil record are in conflict.

The calculus is the story this [the Western] world first told itself as it became the modern world.

Young men wish always to dream of what they have lost. And old men? Of what they have not found.

The desire to see and the desire to ratify what one has seen are desires at odds with one another, if only because they proceed from separate places in the imagination.

The definition of a limit is essentially his [Cauchy's] creation and is as much of a miracle as those fantastic Swiss clocks of the period in which hundreds of gleaming cogs are made to celebrate not only the time and date but the phases of the moon.

Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

The motion of the mind is conveyed along a cloud of meaning.~ There is this paradox that we get to meaning only when we strip the meaning from symbols.

For the most part, it is true, ordinary men and women regard mathematics with energetic distaste, counting its concepts as rhapsodic as cauliflower. This is a mistake-there is no other word. Where else can the restless human mind find means to tie the infinite in a finite bow?

I do not know whether any of this is true. I am certain that the scientific community does not know that it is false.

Although every novel is derived directly from another novel, there is really only one novel, the Quixote.

However good an argument in philosophy may happen to be, it is generally not good enough.

Arithmetic is where the content lies, and not logic but logic prompts certainty, and not arithmetic.