Mathematical Quotes

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That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can.

G. Spencer-Brown

Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulas, are the beginning of every physical theory.

The first process therefore in the effectual study of science must be one of simplification and reduction of results of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis.

James Clerk Maxwell

The chief difficulty of modern theoretical physics resides not in the fact that it expresses itself almost exclusively in mathematical symbols, but in the psychological difficulty of supposing that complete nonsense can be seriously promulgated and transmitted by persons who have sufficient intelligence of some kind to perform operations in differential and integral calculus...

We can now define Mathematical science with precision. It has for its object the indirect measurement of magnitudes, and it proposes to determine magnitudes by each other, according to the precise relations which exist between them.

One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.

A mathematical congress of today reminds one of the Tower of Babel, for few men can follow profitably the discussions of sections other than their own, and even there they are sometimes made to feel like strangers.

It is impossible to study the properties of a single mathematical trajectory. The physicist knows only bundles of trajectories, corresponding to slightly different initial conditions.

Léon Brillouin

It would be difficult to find a greater distance between any two terms than that which separates "matter" in the Greek-medieval tradition and the technical signification, suitably expressed in mathematical symbols, that the word bears in science today.

There are crystals as big as cathedral pillars, delicate as mildew and sharp as needles; plain, blue, green like nothing in the world, of fiery colours or black; mathematical, perfect, like the contrivances of queer and bewildered sages; or recalling livers, hearts, gigantic human organs and animal fluids.

Conclusions based upon analogies may fill up a portion of the vast chasm which separates the certain results of a mathematical natural philosophy from conjectures verging on the extreme, and therefore obscure and barren confines of all scientific development of mind.

Alexander von Humboldt

The spider's web is a glorious mathematical problem.

Jean Henri Fabre

For vacuum rightly conceived of is merely a mathematical quantity extended in the three dimensions, existing per se without heat and cold, soft and hard, rare and dense, and without any natural quality, merely occupying space, as the philosophers maintained before Aristotle, not only within the heavens, but beyond.

Each mathematician for himself, and not anyone for any other, not even all for one, must tread that more than royal road which leads to the palace and sanctuary of mathematical truth.

William Rowan Hamilton

The contemplation of the various steps by which mankind has come into possession of the vast stock of mathematical knowledge can hardly fail to interest the mathematician. He takes pride in the fact that his science, more than any other, is an exact science, and that hardly anything ever done in mathematics has proved to be useless.

History has never regarded itself as a science of statistics. It was the Science of Vital Energy in relation with time; and of late this radiating center of life has been steadily tending, — together with every form of physical and mechanical energy, — toward mathematical expression.

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.

It is important to notice that these badly functioning designs were praised for 'elegance.' But elegance as theoretical scientists apply it is quite different. The elegance of a mathematical formula is that it explains a phenomenon beautifully, with no parts left over. In design, elegance is more readily perceived as a property of product than of process. If we had more elegant theories, we might look to design for more than elegance.

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

Nicholas Murray Butler

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.

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

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

Charles Galton Darwin

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

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 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