American Mathematician Quotes

Kurt Gödel

John Forbes Nash, Jr.

Charles Sanders Peirce

Claude Elwood Shannon

Benoît Mandelbrot

Eugene Wigner

Norbert Wiener

We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.

In the realm of ideas, of mental objects, those ideas whose properties are reproducible are called mathematical objects, and the study of mental objects with reproducible properties is called mathematics.

Philip J. Davis

Proofs really aren't there to convince you that something is true — they're there to show why it is true.

Andrew M. Gleason

Cybernetics is the study of systems and processes that interact with themselves and produce themselves from themselves.

If the sun were created expressly to light and heat the earth, what a waste of energy!

Forest Ray Moulton

He who discovers a fact or makes known a new law or adds a novel beauty to truth in any way makes every one of us his debtor. How beautiful upon the highway are the feet of him who comes bringing in his hands the gift of a new truth to mankind.

Robert Daniel Carmichael

Mathematicians makes natural questions precise.

Richard E. Bellman

The great mathematicians have acted on the principle "Devinez avant de d6montrer," and it is certainly true that almost all important discoveries are made in this fashion.

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

Steven Strogatz

The triplet of specifications - the product-market scope, the growth vector and the competitive advantage - describes the firm's product-market path in the external environment.

Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that need to be done, let him do it himself.

The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.

Claude Elwood Shannon

They used Akbar's principles to formulate a version of Islam that could peacefully co-exist with other religions (or so they claimed). An Emperor's Bequest to Islam, their joint 1,300-page doorstopper, spent twenty weeks on the New York Times bestseller list in hardcover alone. The fact that they remained practicing Muslims (albeit the liberal, wine-guzzling kind) put their message in high international demand.

Moreover, broad plans commensurate with our national purpose and resources would bring conviction of our power to every soldier in the front line, to the nations associated with us in the war, and to the enemy.

Kelly Miller (scientist)

In other words, without a theory, a plan, the mere mechanical manipulation of the numbers in a problem does not necessarily make sense just because you are using Arithmetic!

Lillian Rosanoff Lieber

I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means "to break:" to create irregular fragments... how appropriate for our needs!

Benoît Mandelbrot

Such evidence is not the only kind which produces belief; though positivism maintains that it is the only kind which ought to produce so high a degree of confidence as all minds have or can be made to have through their agreements.

Chauncey Wright

Beauty is very integrated with rarity.... Beauty is connected so much with innovation and priority.... [In mathematics], it has to be something special to make it beautiful. If it's just ordinary, it's not beautiful.

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.

A teacher who is not always thinking about solving problems — ones he does not know the answer to — is psychologically simply not prepared to teach problem solving to his students.

Probably no branch of mathematics has experienced a more surprising growth than has... topology... Considered as a most specialized and abstract subject in the early 1920's, it is today [1938] an indispensable equipment for the investigation of modern mathematical theories.

Raymond Louis Wilder

Yes, but when I discovered it, it stayed discovered.

Concentrate only on the achievements, and ignore the mistakes. When judging a mathematician you should only integrate f+ and ignore the negative part. Perhaps this should apply more generally to all evaluations of your fellow men.

It is possible to believe in progress as a fact without believing in progress as an ethical principle; but in the catechism of many Americans, the one goes with the other.

Each atom of the Holy Spirit is intelligent, and like all other matter has solidity, form, and size, and occupies space.