Mathematical Quotes

500+ Sourced quotes

I had made an empirical discovery and it carried all the weight of a mathematical proof.

On being asked what he meant by the beauty of a mathematical theory of physics, Dirac replied that if the questioner was a mathematician then he did not need to be told, but were he not a mathematician then nothing would be able to convince him of it.

This ambiguity is another example of a growing problem with mathematical notation: There aren't enough squiggles to go around.

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

The domain of physics is no proper field for mathematical pastimes. The best security would be in giving a geometrical training to physicists, who need not then have recourse to mathematicians, whose tendency is to despise experimental science.

To say that mathematics in general has been reduced to logic hints at some new firming up of mathematics at its foundations. This is misleading. Set theory is less settled and more conjectural than the classical mathematical superstructure than can be founded upon it.

Willard van Orman Quine

The laws of nature are but the mathematical thoughts of God.

Man knows only these poor mathematical theories about the heavens, and only God knows the real motions of the heavens and their causes.

Mathematical reasoning is like a long flight of steps; moral, like a short clamber up a craggy rock.

Richard Whately

The future of Thought and therefore of History lies in the hands of physicists, and therefore the future historian must seek his education in the world of mathematical physics.

The Martians seem to have calculated their descent with amazing amazing subtlety — their mathematical learning is evidently far in excess of ours.

I will try by some less mathematical Method than that of mere Numbers, to imprint an Idea in your Mind of the true Extent of the solar System.

Thomas Wright (astronomer)

It seems certain that there is a limit to the amount of living mathematics that humanity can sustain at any time. As new mathematical specialties arise, old ones will have to be neglected.

Trying to capture the physicists' precise mathematical description of the quantum world with our crude words and mental images is like playing Chopin with a boxing glove on one hand and a catcher's mitt on the other.

George Johnson (writer)

Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

It is a remarkable fact that the mathematical inventions which have proved to be most accessible to the masses are also those which exercised the greatest influence on the development of pure mathematics.

No mathematical exactness without explicit proof from assumed principles — such is the motto of the modern geometer.

It is all about numbers. It is all about sequence. It's the mathematical logic of being alive. If everything kept to its normal progression, we would live with the sadness-cry and then walk-but what really breaks us cleanest are the losses that happen out of order.

A hypothesis to gain scientific credence must emerge successful from the test of observed facts and mathematical theory.

The mathematical sciences wield their particular language made of digits and signs, no less subtle than any other.

Jorge Luis Borges

There is nothing physical to be learned a priori. We have no right whatever to ascertain a single physical truth without seeking for it physically, unless it be a necessary consequence of other truths already acquired by experiment, in which case mathematical reasoning is alone requisite.

Peter Guthrie Tait

The distinction between the mathematical method and the scientific is seen in the agonies of very young children to do what their teachers sometimes tell them is mathematics. Anyone who was subjected to elementary geometry when his infantile brain was as unripe as a green walnut will recall the protracted misery he endured.

Eric Temple Bell

The mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the inscrutable meaning of x in nature, but the meaning which x conveys to him.

Arthur Eddington

Calculation touches, at most, certain phenomena of organic destruction. Organic creation, on the contrary, the evolutionary phenomena which properly constitute life, we cannot in any way subject to mathematical treatment.

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.