The only way to learn mathematics is to do mathematics.
For the things of this world cannot be made known without a knowledge of mathematics.
I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.
Sometimes I've believed as many as six impossible things before breakfast.
I hear and I forget. I see and I remember. I do and I understand.
Learning without thought is labor lost; thought without learning is perilous.
Opportunity is missed by most people because it is dressed in overalls and looks like work.
When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity.
Science without religion is lame, religion without science is blind.
The most beautiful thing we can experience is the mysterious. It is the source of all true art and science.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
In a completely rational society, the best of us would be teachers and the rest of us would have to settle for something else.
A teacher affects eternity; he can never tell where his influence stops.
If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
How quick come the reasons for approving what we like!
Man is an artifact designed for space travel. He is not designed to remain in his present biologic state any more than a tadpole is designed to remain a tadpole.
Education is the key to unlock the golden door of freedom.
If your experiment needs statistics, you ought to have done a better experiment.
Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.
I do not believe in the gifted. If [the students] have ganas, I can make them do it.
Logic is invincible, because in order to combat logic it is necessary to use logic.
Poets do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that this danger does lie in logic, not in imagination.
...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
It is the mark of an educated mind to be able to entertain a thought without accepting it.
[Mathematics] is an independent world created out of pure intelligence.
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