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Random Quotation

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

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Loci: Convergence

Mathematical Quotations

Our library of quotations is organized alphabetically by surname of the author.

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Valery, Paul (1871 - 1945)

In the physical world, one cannot increase the size or quantity of anything without changing its quality. Similar figures exist only in pure geometry.


van Vleck, E. B.

This new integral of Lebesgue is proving itself a wonderful tool. I might compare it with a modern Krupp gun, so easily does it penetrate barriers which were impregnable.


Veblen, Thorstein (1857-1929)

The outcome of any serious research can only be to make two questions grow where only one grew before.


Veblen, Thorstein (1857-1929)

Invention is the mother of necessity.


Voltaire (1694-1778)

Vous avez trouve par de long ennuis
Ce que Newton trouva sans sortir de chez lui.
(You have found with much trouble
What Newton found without leaving his home.)
[Written to La Condamine after his measurement of the equator.]


Voltaire (1694-1778)

He who has heard the same thing told by 12,000 eye-witnesses has only 12,000 probabilities, which are equal to one strong probability, which is far from certain.


Voltaire (1694-1778)

There are no sects in geometry.


von Neumann, John (1903 - 1957)

In mathematics you don't understand things. You just get used to them.


John von Neumann

The calculus was the first achievement of modern mathematics, and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.


John von Neumann

Truth is much too complicated to allow anything but approximations.


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