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.
Science without religion is lame, religion without science is blind.
Imagination is more important than knowledge.
Young man, in mathematics you don't understand things. You just get used to them.
Pure mathematics is, in its way, the poetry of logical ideas.
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.
We never know what we are talking about.
Make everything as simple as possible, but not simpler.
Mathematics rightly viewed possesses not only truth but supreme beauty.
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.
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.
Science is what we understand well enough to explain to a computer. Art is everything else we do.
Mathematics is the art of giving the same name to different things.
The mathematician's patterns, like the painter's or the poet's, must be beautiful.
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.
When you can measure what you are speaking about, and express it in numbers, you know something about it.
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.
Obvious is the most dangerous word in mathematics.