Best 579 quotes in «mathematics quotes» category

When we talk mathematics, we may be discussing a secondary language, built on the primary language truly used by the central nervous system. Thus the outward forms of our mathematics are not absolutely relevant from the point of view of evaluating what the mathematical or logical language truly used by the central nervous system is. However, the above remarks about reliability and logical and arithmetical depth prove that whatever the system is, it cannot fail to differ considerably from what we consciously and explicitly consider as mathematics.

While ritual, emotion and reasoning are all significant aspects of human nature, the most nearly unique human characteristic is the ability to associate abstractly and to reason. Curiosity and the urge to solve problems are the emotional hallmarks of our species; and the most characteristically human activities are mathematics, science, technology, music and the arts--a somewhat broader range of subjects than is usually included under the "humanities." Indeed, in its common usage this very word seems to reflect a peculiar narrowness of vision about what is human. Mathematics is as much a "humanity" as poetry.

Yes," I continued, "I discovered this model recently and her style never fails to be mathematically perfect. She seems to come by it naturally. As if she were born resonant. I notice Japanese models tend to do this. Like I said, they seem to have resonance somewhere deep in their culture. But Yuri Nakagawa, she's the best I've ever seen. The best model, with the most powerful resonance. I need her to probe deeper into this profound mathematical instinct, which I call resonance.

A heavy warning used to be given that pictures are not rigorous; this has never had its bluff called and has permanently frightened its victims into playing for safety.

Your Excellency, I have no need of this hypothesis.

You can only be twice someone’s age once.

You too can make the golden cut, relating the two poles of your being in perfect golden proportion, thus enabling the lower to resonate in tune with the higher, and the inner with the outer. In doing so, you will bring yourself to a point of total integration of all the separate parts of your being, and at the same time, you will bring yourself into resonance with the entire universe.... Nonetheless the universe is divided on exactly these principles as proven by literally thousands of points of circumstantial evidence, including the size, orbital distances, orbital frequencies and other characteristics of planets in our solar system, many characteristics of the sub-atomic dimension such as the fine structure constant, the forms of many plants and the golden mean proportions of the human body, to mention just a few well known examples. However the circumstantial evidence is not that on which we rely, for we have the proof in front of us in the pure mathematical principles of the golden mean.

AB=1/4((A+B)^2-(A-B)^2) is an amazing identity, and unfortunately, I have to remind my current students how to prove it.

A chemist who does not know mathematics is seriously handicapped.

[Adams] supposed that, except musicians, everyone thought Beethoven a bore, as every one except mathematicians thought mathematics a bore.

A felicitous but unproved conjecture may be of much more consequence for mathematics than the proof of many a respectable theorem.

A line is length without breadth.

All mathematics is tautology.

A Mathematician is someone who can take a cup of coffee and turn it into a theory.

All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.

All these people that I used to know, they're an illusion to me now. Some are mathematicians, some are carpenters' wives.

A mathematics teacher is a midwife to ideas.

A Miscellany is a collection without a natual ordering relation.

All problems in mathematics are psychological.

All sentences of the type 'deconstruction is X' or 'deconstruction is not X', a priori miss the point, which is to say that they are at least false. As you know, one of the principal things at stake in what is called in my texts 'deconstruction', is precisely the delimiting of ontology and above all of the third-person present indicative: S is P.

A mathematician who is not also something of a poet will never be a complete mathematician.

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.

... 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.

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

A proof tells us where to concentrate our doubts.

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.

... 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 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.

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.

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 .

A thing is obvious mathematically after you see it.

At its heart, music is all higher mathematics.

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

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.

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

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

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.

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.

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

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

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

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

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

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