Mathematical Quotes

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Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.

Leonardo da Vinci

No part of mathematics or mathematical physics involves considerations so strange or so difficult to handle correctly, and there is no subject upon which opinions have been more freely hazarded by the ignorant, or rational dissent more unambiguously expressed by the learned.

Augustus De Morgan

The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work

James Whitbread Lee Glaisher

In a few decades of reconstruction, even the mathematical natural sciences, the ancient archetypes of theoretical perfection, have changed habit completely!

If we are not to live in embarrassed dread in the century ahead, we will have to understand the mathematical ideas that lie behind the scientific advances that are shaping the modern world.

Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings?

In their search for patterns and logical connections, mathematicians face a vast, mysterious ocean of possibilities. Over the centuries, they have discovered an extensive archipelago of truth and beauty. Much of that accumulated knowledge is passed on to succeeding generations. Even more wonders await future explorers of deep, mathematical waters.

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.

From the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life and organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae.

Samuel Taylor Coleridge

Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed.

Albert A. Michelson

For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view.

The theory of perspective was taught in painting schools from the sixteenth century onward according to principles laid down by the masters... However, their treatises on perspective had on the whole been precept, rule, and ad hoc procedure; they lacked a solid mathematical basis. In the period from 1500 to 1600 artists and subsequently mathematicians put the subject on a satisfactory deductive basis, and it passed from quasi-empirical art to a true science. Definitive works on perspective were written much later by eighteenth-century mathematicians Brook Taylor and J. H. Lambert.

We often say that the earth is a sphere, but to be precise, the term sphere refers only to the surface. The correct mathematical term for the solid earth is a ball.

Leonard Susskind

Previous to the time of Pascal, who would have thought of measuring doubt and belief? Who could have conceived that the investigation of petty games of chance would have led to the most sublime branch of mathematical science - the theory of probabilities?

William Stanley Jevons

The limitations of Mathematical science are not, then, in its nature. The limitations are in our intelligence: and by these we find the domain of the science remarkably restricted, in proportion as phenomena, in becoming special, become complex.

In the flowering of a mathematical talent social environment has an important part to play.

Jean Dieudonné

The present tendency of physics is toward describing the universe in terms of mathematical relations between unimaginable entities.

J. W. N. Sullivan

Nature responds only to questions posed in mathematical language, because nature is the domain of measure and order.

Alexandre Koyré

Then suddenly, he was struck by a powerful but simple little truth, and it was this: that English grammar is governed by rules that are almost mathematical in their strictness!

In mathematics, granted that we are giving any serious attention to mathematical ideas, the symbolism is invariably an immense simplification.

Alfred North Whitehead

To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography.

Mathematical training is almost purely deductive. The mathematician starts with a few simple propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them.

Thomas Henry Huxley

Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.

The orthodox believers in God are divided into two camps, one of which maintains that the existence of God is as demonstrable as any mathematical proposition, while the other asserts that his existence is not demonstrable to the intellect.

Shameless ignorance in regard to such serious intellectual conquests as are embodied in the mathematical literature does not represent a normal condition on the part of those interested in the history of the human race.

George Abram Miller