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Teaching is the royal road to learning.
Sep 21, 2025
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.
A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.
Geometry is the foundation of all painting.
Mighty is geometry; joined with art, resistless.
Where there is matter, there is geometry.
We never know what we are talking about.
Mathematics is the supreme judge; from its decisions there is no appeal.
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
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.
But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Mathematics consists in proving the most obvious thing in the least obvious way.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
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.
The only way to learn mathematics is to do mathematics. That tenet is the foundation of the do-it-yourself, Socratic, or Texas method.
Geometry is the science of correct reasoning on incorrect figures.
Mathematics is the art of giving the same name to different things.
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Nothing enrages me more than when people criticize my criticism of school by telling me that schools are not just places to learn maths and spelling, they are places where children learn a vaguely defined thing called socialization...I think schools generally do an effective and terribly damaging job of teaching children to be infantile, dependent, intellectually dishonest, passive and disrespectful to their own developmental capacities.
Young man, in mathematics you don't understand things. You just get used to them.
A circle is a round straight line with a hole in the middle.
Learning without thought is labor lost; thought without learning is perilous.
How is it that little children are so intelligent and men so stupid? It must be education that does it.
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.
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.
I think that great programming is not all that dissimilar to great art. Once you start thinking in concepts of programming it makes you a better person...as does learning a foreign language, as does learning math, as does learning how to read.
I hear and I forget. I see and I remember. I do and I understand.
Education is not preparation for life; education is life itself.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
Obvious is the most dangerous word in mathematics.
Arithmetic is where numbers fly like pigeons in and out of your head.
Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.
Angling may be said to be so like the mathematics that it can never be fully learned.
[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.
Mathematics is like draughts in being suitable for the young, not too difficult, amusing, and without peril to the state.
Education is the key to unlock the golden door of freedom.
The only way to learn mathematics is to do mathematics.
Education is what remains after one has forgotten what one has learned in school.
Every child is an artist. The problem is how to remain an artist once we grow up.
It is a miracle that curiosity survives formal education.
Education is what survives when what has been learned has been forgotten.
The illiterate of the 21st century will not be those who cannot read and write, but those who cannot learn, unlearn, and relearn.
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