What is now proved was once only imagin'd.

What is now proved was once only imagin'd.

The Marriage of
Heaven and Hell,
1790-1793

Angling may be said to be so like mathematics that it can never be fully learned.

The Compleat Angler, 1653.

For twenty pages perhaps, he read slowly, carefully, dutifully, with pauses for self-examination and working out examples. Then, just as it was working up and the pauses should have been more scrupulous than ever, a kind of swoon and ecstasy would fall on him, and he read ravening on, sitting up till dawn to finish the book, as though it were a novel. After that his passion was stayed; the book went back to the Library and he was done with mathematics till the next bout. Not much remained with him after these orgies, but something remained: a sensation in the mind, a worshiping acknowledgment of something isolated and unassailable, or a remembered mental joy at the rightness of thoughts coming together to a conclusion, accurate thoughts, thoughts in just intonation, coming together like unaccompanied voices coming to a close.

Mr. Fortune's Maggot.

Theology, Mr. Fortune found, is a more accommodating subject than mathematics; its technique of exposition allows greater latitude. For instance when you are gravelled for matter there is always the moral to fall back upon. Comparisons too may be drawn, leading cases cited, types and antetypes analysed and anecdotes introduced. Except for Archimedes mathematics is singularly naked of anecdotes.

Mr. Fortune's Maggot.

He resumed:

"In order to ascertain the height of the tree I must be in such a position that the top of the tree is exactly in a line with the top of a measuring stick or any straight object would do, such as an umbrella which I shall secure in an upright position between my feet. Knowing then that the ratio that the height of the tree bears to the length of the measuring stick must equal the ratio that the distance from my eye to the base of the tree bears to my height, and knowing (or being able to find out) my height, the length of the measuring stick and the distance from my eye to the base of the tree, I can, therefore, calculate the height of the tree."

"What is an umbrella?"

Mr. Fortune's Maggot.

What if angry vectors veer

Round your sleeping head, and form.

There's never need to fear

Violence of the poor world's abstract storm.

Lullaby in
Encounter, 1957.

Every mathematician worthy of the name has experienced ... the state of lucid exaltation in which one thought succeeds another as if miraculously ... This feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work ....

The Apprenticeship
of a Mathematician.

Algebra and money are essentially levelers; the first intellectually, the second effectively.

W. H. Auden and L.
Kronenberger, The
Viking Book of
Aphorisms, New York:
Viking Press, 1966.

Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.

Miss Lonelyhearts.

Our federal income tax law defines the tax y to be paid in terms of the income x; it does so in a clumsy enough way by pasting several linear functions together, each valid in another interval or bracket of income. An archeologist who, five thousand years from now, shall unearth some of our income tax returns together with relics of engineering works and mathematical books, will probably date them a couple of centuries earlier, certainly before Galileo and Vieta.

The Mathematical Way of Thinking, an address given at the Bicentennial Conference at the University of Pennsylvania, 1940.