The true spirit of delight, the exaltation, the sense of being more than
man, which is the touchstone of the highest excellence,
is to be found in **mathematics** as surely as in
poetry.

**mathematics** is the door and key to the sciences.

All science requires **mathematics**?the knowledge of mathematical things
is almost innate in us?this is the easiest of
sciences. A fact which is obvious in that no one's brain rejects
it. For laymen and people who are utterly illiterate
know how to count and reckon.

Angling may be saidtobe so like**mathematics**, that itcan never be fully
learnt.

All things began in order, so shall they end, and so shall they begin again;
according to the ordainer of order and mystical
**mathematics** of the city of heaven.

If you refuse to study anatomy, the arts of drawing and perspective, the **mathematics** of aesthetics, and the science of color, let me tell you that this is more a sign of laziness than of genius.

To those who ask what the infinitely small quantity in **mathematics** is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.

Trivialism arises from the idea that **mathematics** is classical and there is contradiction in **mathematics**, and therefore (under our old classical reasoning), all of **mathematics** is true , we then get to the meaninglessness of any particular mathematical statement and wallow in our degenerate theory .

Theorems often tell us complex truths about the simple things, but only rarely tell us simple truths about the complex ones. To believe otherwise is wishful thinking or "**mathematics** envy."

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of **mathematics**, for it is equally true of every other exclusive occupation. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.

It wasn't by accident that the Gettysburg address was so short. The laws of prose writing are as immutable as those of flight, of **mathematics**, of physics.

There is no branch of **mathematics**, however abstract, which may not some day be applied to phenomena of the real world.

**mathematics** is the science which draws necessary conclusions.

There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, **mathematics**, and chess.

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?

Regardless of whether or not God exists, God has no place in **mathematics**, at least in my book.

We had principles in **mathematics** that were granted to be absolute in **mathematics** for over 800 years, but new science has gotten rid of those absolutism, gotten forward other different logics of looking at **mathematics**, and sort of turned the way we look at it as a science altogether after 800 years.

In my youth it was said that what was too silly to be said may be sung. In modern economics it may be put into **mathematics** .

Mathemagical **mathematics** combines the beauty of mathematical structure with the entertainment value of a trick.

At present, when the prevailing forms of society have become hindrances to the free expression of human powers, it is precisely the abstract branches of science, **mathematics** and theoretical physics, which ... offer a less distorted form of knowledge than other branches of science which are interwoven with the pattern of daily life, and the practicality of which seemingly testifies to their realistic character.

**mathematics** is the bold luxury of pure reason, one of the few that remain today.

It seems to me now that **mathematics** is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true.

Concern for the symbol has completely disappeared from our science . And yet, if one were to give oneself the trouble, one could easily find, in certain parts at least of contemporary **mathematics**... symbols as clear, as beautiful, and as full of spiritual meaning as that of the circle and mediation. From modern thought to ancient wisdom the path would be short and direct, if one cared to take it.

Math is perfect (in principle), but mathematicians are not (because they are humans), hence the **mathematics** that (human) mathematicians do is influenced by the weltanschauung of the people around them.

The terms synthesis and analysis are used in **mathematics** in a more special sense than in logic. In ancient **mathematics** they had a different meaning from what they now have. The oldest definition of mathematical analysis as opposed to synthesis is that given in Euclid , XIII. 5, which in all probability was framed by Eudoxus: "Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth; synthesis is the obtaining of the thing sought by reasoning up to the inference and proof of it."

The Greeks... discovered **mathematics** and the art of deductive reasoning. Geometry, in particular, is a Greek invention, without which modern science would have been impossible.

The land of easy **mathematics** where he who works adds up and he who retires subtracts.

Mechanical Engineering may be defined as being the application of **mathematics** to Science, with particular reference to the design and fabrication of all forms of machinery. Since engineering is the combined science and art of utilizing the

School children and students who love God should never say: “For my part I like **mathematics**”; “I like French”; “I like Greek.” They should learn to like all these subjects, because all of them develop that faculty of attention which, directed toward God, is the very substance of prayer.

The significant contribution to **mathematics** we owe to the Arabs was to absorb Greek and Hindu **mathematics**, preserve it, and ultimately, through events we have yet to look in, transmit it to Europe. (...) In Spain the Arabs were constantly attacked and finally conquered in 1492 by the Christians; this ended the mathematical and scientific activity in the region.