Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him...

I have stressed this distinction because it is an important one. It defines the fundamental difference between probability and statistics: the former concerns predictions based on fixed probabilities; the latter concerns the inference of those...

Whereas Nature does not admit of more than three dimensions … it may justly seem very improper to talk of a solid … drawn into a fourth, fifth, sixth, or further dimension.

I guess I think of lotteries as a tax on the mathematically challenged.

If one is working from the point of view of getting beauty into one’s equation, … one is on a sure line of progress.

Das ist nicht Mathematik, das ist Theologie.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker...

Mathematics effectively began when a few Greek friends got together to talk about numbers and lines and angles.

a fresh mind adds a better mathematic ability #Bweqy

It was as though applied mathematics was my spouse, and pure mathematics was my secret lover.

To return to the general analysis of the Rosicrucian outlook. Magic was a dominating factor, working as a mathematics-mechanics in the lower world, as celestial mathematics in the celestial world, and as angelic conjuration in...

University President: Why is it that you physicists always require so much expensive equipment? Now the Department of Mathematics requires nothing but money for paper, pencils, and erasers…and the Department of Philosophy is better still....

Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view.

I’m sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that...

God made the integers; all the rest is the work of Man.

I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed...

Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry … because they said it was so UTTERLY...

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

The spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern...

Just as all things speak about God to those that know Him, and reveal Him to those that love Him, they also hide Him from all those that neither seek nor know Him.

College is the grinding machine of the Mathematical Establishment, a conveyor belt that takes individuals from one cookie cutter to another so that the product comes within tight control limits out of the assembly line.

My mathematics is simple: one plus one = one.

I then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away...

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.

Amusement if one of humankind’s strongest motivational forces.

Tengo’s lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the...

Mathematics should be studied if only for that it puts the mind in order.

[When asked why are numbers beautiful?]It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing...

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton’s good luck to come at...

Why don’t we want our children to learn to do mathematics? Is it that we don’t trust them, that we think it’s too hard? We seem to feel that they are capable of making arguments...

{Before the time of it never occurred to anyone that mathematical research} was one of the things for which a mathematical department existed. Today it is a commonplace in all the leading universities. Peirce stood...

Beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds...

Obscenity is a function of culture – a function in the mathematical sense, I mean, its value changing with that of the variables on which it depends.

He is like the fox, who effaces his tracks in the sand with his tail.{Describing the writing style of famous mathematician Carl Friedrich Gauss}

But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they...

An arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn...

When one day Lagrange took out of his pocket a paper which he read at the Académe, and which contained a demonstration of the famous Postulatum of Euclid, relative to the theory of parallels. This...

If you can’t test it, it’s not theorics — it’s metatheorics. A branch of philosophy. So, if you want to think of it this way, our test equipment is what defines the boundary separating theorics...

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a...

. . . the world in which we live has an increasing number of feedback loops, causing events to be the cause of more events (say, people buy a book because other people bought it),...

No old Men (excepting Dr. Wallis) love Mathematicks.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being...

One cool thing about mathematics is they (the audience) don’t have to be able to understand math to see the passion that makes it so exciting to them.

Nobody before the Pythagorean had thought that mathematical relations held the secret of the universe. Twenty-five centuries later, Europe is still blessed and cursed with their heritage. To non-European civilizations, the idea that numbers are...

The astonishing fact is that similar mathematics applies so well to planets and to clocks. It needn’t have been this way. We didn’t impose it on the Universe. That’s the way the Universe is. If...

CSIR-UGC NET exam is being rated as one of the most challenging competitive exams, however it is not that difficult to clear once you have an experienced and trusted adviser who can help you choose...

If you plug in a number and the math starts getting creepy (anything involving fractions or negative numbers is creepy)…

This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will...

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would...