Explore Quotes on Mathematics

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.

Mere poets are sottish as mere drunkards are, who live in a continual mist, without seeing or judging anything clearly. A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure a mathematical head, to be a complete and excellent poet.

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.

Prayers for the condemned man will be offered on an adding machine. Numbers constitute the only universal language.

Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.

The greatest reward lies in making the discovery; recognition can add little or nothing to that.

The physical five oranges goes up the ladder to the picture of the five oranges which goes up to the representation of the five oranges as a numeral. This points in the direction of a definition of abstraction: when we abstract we voluntarily ignore details of a context, so that we can accomplish a goal.

In studying mathematics or simply using a mathematical principle, if we get the wrong answer in sort of algebraic equation, we do not suddenly feel that there is an anti-mathematical principle that is luring us into the wrong answers.

Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders.

All those formal systems, in mathematics and physics and the philosophy of science, which claim to give foundations for certain truth are surely mistaken. I am tempted to say that we do not look for truth, but for knowledge. But I dislike this form of words, for two reasons. First of all, we do look for truth, however we define it, it is what we find that is knowledge. And second, what we fail to find is not truth, but certainty; the nature of truth is exactly the knowledge that we do find.

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

At the age of 12, I developed an intense interest in mathematics. On exposure to algebra, I was fascinated by simultaneous equations and read ahead of the class to the end of the book.

I had changed from being a mathematician to a practicing scientist. I was increasingly embarassed that I could no longer follow some of the more modern branches of pure mathematics.

We find that at present the human race is divided politically into one wise man, nine knaves, and ninety fools out of every hundred. That is, by an optimistic observer. The nine knaves assemble themselves under the banner of the most knavish among them, and become politicians; the wise man stands out, because he knows himself to be hopelessly out-numbered, and devotes himself to poetry, mathematics or philosophy; while the ninety fools plod off behind the banners of the nine villains, according to fancy, into the labyrinths of chicanery, malice and warfare.

Those who are accustomed to judge by feeling do not understand the process of reasoning, because they want to comprehend at a glance and are not used to seeking for first principles. Those, on the other hand, who are accustomed to reason from first principles do not understand matters of feeling at all, because they look for first principles and are unable to comprehend at a glance.

In the study of ideas, it is necessary to remember that insistence on hard-headed clarity issues from sentimental feeling, as it were a mist, cloaking the perplexities of fact. Insistence on clarity at all costs is based on sheer superstition as to the mode in which human intelligence functions. Our reasonings grasp at straws for premises and float on gossamers for deductions.

The mathematician who pursues his studies without clear views of this matter, must often have the uncomfortable feeling that his paper and pencil surpass him in intelligence.

I recall once saying that when I had given the same lecture several times I couldn't help feeling that they really ought to know it by now.