American Mathematician Quotes

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.

With the extremely small or the extremely large, with inconceivably brief or extended phenomena, science has a difficult time. It is by no means clear that our present concepts or even our existing language is suitable for these ranges.

It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature.

By slow degrees, the minds of men were cut adrift from their old scholastic moorings and sent forth on the wide sea of scientific inquiry, to discover new islands and continents of truth.

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.

Mathematics is the codified body of all logical thought.

George David Birkhoff

The better theories are verifiable. Once upon a time that was the sine qua non of any theory. Nowadays, addressing events at the Big Bang, we face, perhaps for the first time, a situation in which a theory may never be experimentally tested.

Leon M. Lederman

The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.

Most convincing to me of the spiritual relations between mathematics and music, is my own very personal experience. Composing in an amateurish way, I get exactly the same elevation from a prelude that has come to me at the piano, as I do from a new idea that has come to me in mathematics.

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)

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.

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

Andrew M. Gleason

The characteristic which distinguishes the present-day professional statistician, is his interest and skill in the measurement of the fallibility of conclusions.

George W. Snedecor

It is a paradox in mathematics and physics that we have no good model for the teaching of models.

Hartley Rogers Jr.

Virtually every discipline and endeavor is presently under a naturalistic pall.

William A. Dembski

Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?

Edward Norton Lorenz

I cannot imagine that I shall ever return to the creed of the true Platonist, who sees the world of the actual infinite spread out before him and believes that he can comprehend the incomprehensible.

Abraham Robinson

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.

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

Mathematics is the science of order and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations.

Shlomo Sternberg

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

The fundamental importance of the subject of order may be inferred from the fact that all the concepts required in geometry can be expressed in terms of the concept of order alone.

Edward Vermilye Huntington

Authors who discover formulas should not rush into print. Even as in business and marriage, in mathematics not all that is true needs to be published.

Underwood Dudley

And I'm a stodgy old scientist who believes, naively, that there exists an external world, that there exist objective truths about that world, and that my job is to discover some of them.