Obvious is the most dangerous word in mathematics.

The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

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

Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.

Arithmetic is where numbers fly like pigeons in and out of your head.

We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years.

Mighty is geometry; joined with art, resistless.

Geometry is the foundation of all painting.

But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.

The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.

Education is learning more than it is being taught. It's the chemistry of curiosity exposed to information. In that sense all of life is potentially school. And even I can pass that.

Education is not preparation for life; education is life itself.

How is it that little children are so intelligent and men so stupid? It must be education that does it.

Education is the key to unlock the golden door of freedom.

It is a miracle that curiosity survives formal education.

The only way to learn mathematics is to do mathematics.

I hear and I forget. I see and I remember. I do and I understand.

Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.

Mathematics is a game played according to certain simple rules with meaningless marks on paper.

Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.

Learning without thought is labor lost; thought without learning is perilous.

Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.

Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.

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