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

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 queen of the sciences.

**Mathematics** is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.

**Mathematics** knows no races or geographic boundaries; for **Mathematics**, the cultural world is one country.

"**Mathematics** is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.

**Mathematics** is the gate and key of the sciences... Neglect of **Mathematics** works injury to all knowledge , since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.

**Mathematics** is good for the soul, getting things right enlivens a sense of truth, efforts to understand automatically purify desires.

[There is] a delusion that macro-economics is both viableanduseful (a
delusionencouraged by its extensive use of **Mathematics**,
which must always impress politicians lacking
any mathematical education, and which is really the
nearest thing to the practice of magic that occurs among
professional economists).

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.

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.

Toward the end of his life, Gödel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in **Mathematics**, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt Gödel's gifts might be aborted.

A good mathematical joke is better, and better **Mathematics**, than a dozen mediocre papers.

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

Poetry is a sort of inspired **Mathematics**, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.

In many cases, **Mathematics** is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.

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.

To those who do not know **Mathematics** it is difficult to get across a real feeling as to the beauty , the deepest beauty, of nature . ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

As soon as a thought or word becomes a tool, one can dispense with actually ‘thinking’ it, that is, with going through the logical acts involved in verbal formulation of it. As has been pointed out, often and correctly, the advantage of **Mathematics** the model of all neo-positivistic thinking lies in just this ‘intellectual economy.’ Complicated logical operations are carried out without actual performance of the intellectual acts upon which the mathematical and logical symbols are based. … Reason … becomes a fetish, a magic entity that is accepted rather than intellectually experienced.

The idea of an isolated American painting , so popular in this country during the thirties, seems absurd to me, just as the idea of a purely American **Mathematics** or physics would seem absurd... And in another sense, the problem doesn’t exist at all; or, if it did, would solve itself: An American is an American and his painting would naturally be qualified by the fact, whether he wills or not. But the basic problems of contemporary painting are independent of any one country.

It was, however, from Spain, and not from Arabia, that a knowledge of eastern **Mathematics** first came into western Europe. The Moors had established their rules in Spain in 747, and by the tenth or eleven century had attained a high degree of civilisation.

In **Mathematics** the art of asking questions is more valuable than solving problems.

(Econometrics is) the unification of economic theory, statistics and **Mathematics** .

Even in **Mathematics** his whimsical fancy was sometimes suffered to peep out, and little girls who learnt the rudiments of calculation at his knee found the path they had imagined so thorny set about with roses by reason of the delightful fun with which he would turn a task into a joy. But when the fun was over the little girl would find that she had learnt the lesson (all unknowingly) just the same. Happy little girls who had such a master.

Questions that pertain to the foundations of **Mathematics**, although treated by many in recent times, still lack a satisfactory solution. Ambiguity of language is philosophy's main source of problems. That is why it is of the utmost importance to examine attentively the very words we use.

Pythagoras raised **Mathematics** to the rank of a science. Arithmetic was courted by him as fervently as geometry. In fact, arithmetic is the foundation of his philosophic system.

Tantra is a very very poetic approach, not arithmetical. And tantra believes in love, not in **Mathematics**. It believes in sudden enlightenment.

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

Men are constantly attracted and deluded by two opposite charms: the charm of competence which is engendered by **Mathematics** and everything akin to **Mathematics**, and the charm of humble awe, which is engendered by meditation on the human soul and its experiences. Philosophy is characterized by the gentle, if firm, refusal to succumb to either charm.

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 .