Best 579 quotes in «mathematics quotes» category

A Miscellany is a collection without a natual ordering relation.

... and it is probably that there is some secret here which remains to be discovered.

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.

A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence.

At its heart, music is all higher mathematics.

A proof tells us where to concentrate our doubts.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

A thing is obvious mathematically after you see it.

Applied mathematics will always need pure mathematics just as anteaters will always need ants.

... a result once generally accepted by mathematicians is seldom retracted, and then only with great pangs. The Nature of Mathematics

Arithmetic is where the content lies, and not logic; but logic prompts certainty, and not arithmetic.

As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence.

As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

a straight line is the shortest possible line between any two points - an axiom equally true in morals as in mathematics.

Before creation, God did just pure mathematics. Then He thought it would be a pleasant change to do some applied.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Bacon not only despised the syllogism, but undervalued mathematics, presumably as insufficiently experimental. He was virulently hostile to Aristotle , but he thought very highly of Democritus , Although he did not deny that the course of nature exemplifies a Divine purpose, he objected to any admixture of teleological explanation in the actual investigation of phenomena; everything, he held, should be explained as following necessarily from efficient causes .

Do mathematics have a relation to reality or are they only a mathematical symbol?

But anything that can be called "rigor" is lost exactly where the things become interesting and non trivial.

Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.

Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.

Chess, like mathematics and music, is a nursery for child prodigies.

... combinatorics, a sort of glorified dice-throwing.

Computation involves going from a question to an answer. Mathematics involves going from an answer to a question.

Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.

Die mathematische Forschung besteht aus 10% Intuition und 90% Arbeit.

Do not lose your faith. A mighty fortress is our mathematics. Mathematics will rise to the challenge, as it always has.

Do not mathematics and all sciences seem full of contradictions and impossibilities to the ignorant, which are all resolved and cleared to those that understand them?

But I quite like the way you can talk about science without necessarily using mathematics, but using metaphors instead.

Certainly the best times were when I was alone with mathematics, free of ambition and pretense, and indifferent to the world.

Do not trust financial market risk models. Despite the predilection of some analysts to model the financial markets using sophisticated mathematics, the markets are governed by behavioral science, not physical science.

Equations are just the boring part of mathematics. I attempt to see things in terms of geometry.

Even in pure mathematics they can't remove all paradox, and the rest of us should also recognize we are going to have to endure a lot of paradox, like it or not.

Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?

Every dimension is special.

Everything tries to be round.

Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics.

Every human activity, good or bad, except mathematics, must come to an end.

Examples ... which might be multiplied ad libitum, show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.

Except in pure mathematics, nothing is known for certain (although much is certainly false).

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

...from the same principles, I now demonstrate the frame of the System of the World.

From nothing I have created another entirely new world.

Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

Geometry is the archetype of the beauty of the world.

God ever arithmetizes.

Have you ever observed that we pay much more attention to a wise passage when it is quoted, than when we read it in the original author?

Here, where we reach the sphere of mathematics, we are among processes which seem to some the most inhuman of all human activities and the most remote from poetry. Yet it is here that the artist has the fullest scope of his imagination.

Here is something Category-Theorists like: it is trivial, but not trivially trivial.

[I can] scarcely write upon mathematics or mathematicians. Oh for words to express my abomination of the science.