Mathematical Quotes

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[The Riemann Hypothesis has] no longer just analytic number theorists involved, but all mathematicians know about the problem, and many realize that they may have useful insights to offer. As far as I can see, a solution is as likely to come from a probabilist, geometer or mathematical physicist, as from a number theorist.

Roger Heath-Brown

This intuition of mathematical order, which enables us to perceive harmonies and hidden relations, cannot be present in everyone.

Henri Poincaré

One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

Wheresoever the carcass is, there will the eagles be gathered together, and where the symbols of the mathematical physicists flock, there presumably is some prey for them to settle on, which the plain man at least will prefer to call by a name suggestive of something more than passive emptiness.

Arthur Eddington

Toward the end of the last century, many physicists felt that the mathematical description of physics was getting ever more complicated. Instead, the mathematics involved has become ever more abstract, rather than more complicated. The mind of God appears to be abstract but not complicated. He also appears to like group theory.

Frank Lloyd Wright

The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures.

It will seem not a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impressions on the senses.

The greatest writers on mathematical subjects have a genius which saves them from their own slips, and guides them to true results through inaccurate expression, and sometimes through absolute error.

Augustus De Morgan

The knowledge that is suited to our situation and powers, the whole compass of moral, natural, and mathematical science, was neglected by the new Platonists; whilst they exhausted their strength in the verbal disputes of metaphysics, attempted to explore the secrets of the invisible world, and studied to reconcile Aristotle with Plato, on subjects of which both these philosophers were as ignorant as the rest of mankind.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

Nicholas Murray Butler

Every new body of discovery is mathematical in form, because there is no other guidance we can have.

Charles Galton Darwin

Our world rests on mathematical foundations, and mathematics is unavoidably embedded in our global culture.

To the author the main charm of probability theory lies in the enormous variability of its applications. Few mathematical disciplines have contributed to as wide a spectrum of subjects, a spectrum ranging from number theory to physics, and even fewer have penetrated so decisively the whole of our scientific thinking.

The mathematician's best work is art... a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other.

Gösta Mittag-Leffler

In all ages and countries where learning hath prevailed, the mathematical sciences have been looked upon as the most considerable branch of it.

The seeds from Ramanujan's garden have been blowing on the wind and have been sprouting all over the landscape.
[On the stimulating effects of Ramanujan's mathematical legacy.]

Mathematics... is mired in a language of symbols foreign to most of us, [it] explores regions of the infinitesimally small and the infinitely large that elude words, much less understanding. So specialized is mathematics today... that most mathematical papers appearing in most mathematics journals are indecipherable even to most mathematicians.

He said that new systems of nature were but new fashions, which would vary in every age; and even those who pretend to demonstrate them from mathematical principles, would flourish but a short period of time, and be out of vogue when that [system of nature] was determined.

It can hardly be disputed that nature and our conscious mathematical minds work according to the same laws.

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

Deductive reasoners, those who cultivate science, of whatever kind, by means of mathematical and logical processes alone, may acquire an exaggerated feeling of the amount and value of their labours.

William Whewell

As long as you are occupied with the mathematical sciences and the technique of logic, you belong to those who walk around the palace in search of the gate.... When you complete your study of the natural sciences and get a grasp of the metaphysics, you enter into the inner courtyard and are in the same house as [God] he.

Engineering then is not merely a mathematical science. It must be approached with a sense of proportion and aesthetics.

In order that a mathematical science of any importance may be founded upon conventional definitions, the entities created by them must have properties which bear some affinity to the properties of existing things.

Alfred North Whitehead

Who is so unfortunate as not to know something of the religious awe, the solace and the peace that come from cloistral contemplation of the purity and everlastingness of mathematical truth?

Cassius Jackson Keyser