Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity and split into diverse branches.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus as well as analytical geometry.

Projective geometry has opened up for us with the greatest facility new territories in our science and has rightly been called the royal road to our particular field of knowledge.

In mathematics we have long since drawn the rein, and given over a hopeless race.

In mathematics the art of proposing a question must be held of higher value than solving it.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

Mathematics is as old as Man.

I finally reached the conclusion that mathematics was the study I was best fitted to follow, though I did not clearly see in what way I should turn the subject to account.

As the existence of a corps of professors of mathematics is peculiar to our navy, as well as an apparent, perhaps a real, anomaly, some account of it may be of interest.

Now being in such grace and favor by reason I learned him some points of geometry and understanding of the art of mathematics with other things, I pleased him so that what I said he would not contrary.

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.

I read one or two other books which gave me a background in mathematics other than logic.

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.

Life has obliged him to remember so much useful knowledge that he has lost not only his history, but his whole original cargo of useless knowledge; history, languages, literatures, the higher mathematics, or what you will - are all gone.

How is an error possible in mathematics?

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

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.

I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so.

If a man's wit be wandering, let him study the mathematics.

Reading music is something that's inherently hateful to me. It makes music like mathematics.

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.

Mathematics is the art of giving the same name to different things.

You can not apply mathematics as long as words still becloud reality.

My interest in the sciences started with mathematics in the very beginning, and later with chemistry in early high school and the proverbial home chemistry set.

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

Mathematics allows for no hypocrisy and no vagueness.

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 poetry.

Mathematics is the most beautiful and most powerful creation of the human spirit.

Angling may be said to be so like the mathematics that it can never be fully learned.

Mathematics is the music of reason.

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.

Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.

Film is one of the three universal languages, the other two: mathematics and music.

For the things of this world cannot be made known without a knowledge of mathematics.

We must always emphasize research and development of science and mathematics, and I can think of no better way to achieve this than through our future in space.

God used beautiful mathematics in creating the world.

I read everything: fiction, history, science, mathematics, biography, travel.

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.

Mathematics is written for mathematicians.

I did not have a very literary background. I came to poetry from the sciences and mathematics, and also through an interest in Japanese and Chinese poetry in translation.

The essence of mathematics lies in its freedom.

Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.

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.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.