The issue, then, is not, What is the best way to teach? but, What is mathematics really all about?… Controversies about…teaching cannot be resolved without confronting problems about the nature of mathematics.

The thing I want you especially to understand is this feeling of divine revelation. I feel that this structure was “out there” all along I just couldn’t see it. And now I can! This is...

Adaptability to change is itself a hallmark of successful education.

But there is another reason for the high repute of mathematics: it is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.

I studied mathematics which is the madness of reason.

The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world by mathematical formulas. Only money economy has filled the days of...

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little...

Réduites à des théories générales, les mathématiques seraient une belle forme sans contenu.Reduced to general theories, mathematics would be a beautiful form without content.

[I was advised] to read Jordan’s ‘Cours d’analyse’; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for...

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical...

Jack had wondered how geometers could be so inventive as to produce so many types and families of curves. Later he had come to perceive that of curves there was no end, and the true...

Increasingly, the mathematics will demand the courage to face its implications.

the theorem of incompleteness . . . [shows] there is nothing on this level of existence that can fully explain this level of existence.

Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of words.

Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music,...

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.

What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?

In short, if we adhere to the standard of perfection in all our endeavors, we are left with nothing but mathematics and the White Album.

Mathematics has always shown a curious ability to be applicable to nature, and this may express a deep link between our minds and nature. We are the Universe speaking out, a part of nature. So...

Mathematics, which most of us see as the most factual of all sciences, constitutes the most colossal metaphor imaginable, and must be judged, aesthetically as well as intellectually in terms of the success of this...

I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made...

Poincaré [was] the last man to take practically all mathematics, pure and applied, as his province. … Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in...

The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first...

The important thing to remember about mathematics is not to be frightened

There have been many authorities who have asserted that the basis of science lies in counting or measuring, i.e. in the use of mathematics. Neither counting nor measuring can however be the most fundamental processes...

The only problem i had with literature that I simply couldn’t figure out was that the correct answer was the first thing that comes to your mind after reading the question, the most obvious one....

A mathematician is an individual who calls himself a ‘physicist’ and does ‘physics’ and physical experiments with abstract concepts.

I only know that when I study mathematics, I transport myself to another world, a world of exquisite beauty and truth. And in that world I am the person I like to be.

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, … the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its...

I hate math. It’s hard, it’s stupid, and it’s nature’s way of separating spinsters from women who end up breeding.

A key ingredient in appreciating what mathematics is about is to realize that it is concerned with ideas, understanding, and communication more than it is with any specific brand of symbols….It is almost as if...

In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians’ scientific interest in pure mathematics for its own sake. I have...

And, most important of all,” added the Mathemagician, “here is your own magic staff. Use it well and there is nothing it cannot do for you.”He placed in Milo’s breast pocket a small gleaming pencil...

Zero is a black hole of mathematics.

Le Verrier—without leaving his study, without even looking at the sky—had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.

Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

To the extent math refers to reality, we are not certain; to the extent we are certain, math does not refer to reality.

Mathematics is the science which draws necessary conclusions.

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression,more exact,compact, and ready than ordinary language. The great body of physical...

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact,...

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

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

Existe una opinión generalizada según la cual la matemática es la ciencia más difícil cuando en realidad es la más simple de todas. La causa de esta paradoja reside en el hecho de que, precisamente...

Mathematics had never had more than a secondary interest for him [her husband, George Boole]; and even logic he cared for chiefly as a means of clearing the ground of doctrines imagined to be proved,...

Although personally, I think cyberspace means the end of our species.

Mathematics … is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.

I had a feeling once about Mathematics – that I saw it all. Depth beyond depth was revealed to me – the Byss and Abyss. I saw – as one might see the transit of...