The desire to understand the world and the desire to reform it are the two great engines of progress.

The desire to understand the world and the desire to reform it are the two great engines of progress.

Marriage and Morals.

It can be shown that a mathematical web of some kind can be woven about any universe containing several objects. The fact that our universe lends itself to mathematical treatment is not a fact of any great philosophical significance.

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

If your experiment needs statistics, you ought to have done a better experiment.

In N. T. J. Bailey the Mathematical Approach to Biology and Medicine, New York: Wiley, 1967.

Calculus is the culmination of a dramatic intellectual struggle which has lasted for over 2500 years and has proved itself to be the greatest achievement of western civilization.

Richard Courant

The interplay between generality and individuality, deduction and construction, logic and imagination - this is the profound essence of live mathematics. Any one or another of these aspects of mathematics can be at the center of a given achievement. In a far reaching development all of them will be involved. Generally speaking, such a development will start from the "concrete" ground, then discard ballast by abstraction and rise to the lofty layers of thin air where navigation and observation are easy; after this flight comes the crucial test of landing and reaching specific goals in the newly surveyed low plains of individual "reality." In brief, the flight into abstract generality must start from and return again to the concrete and specific.

Richard Courant

We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist; but if a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic musical.

Ralph Waldo Emerson

There is, thus, a hidden circularity in formal mathematical exposition. The theorems are proved starting with definitions; but the definitions themselves are motivated by the theorems that we have previously decided ought to be correct.

*Indiscrete Thoughts* (Birkhauser Boston, 1997), p. 97

There is nothing more deadly for a non-professional mathematician than being assaulted by a rigorous version of facts which have always been obvious.

*Indiscrete Thoughts* (Birkhauser Boston, 1997), p. 245

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