Pure mathematics is, in its way, the poetry of logical ideas.
Imagination is more important than knowledge.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
I must study politics and war that my sons may have liberty to study mathematics and philosophy.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
Mathematics rightly viewed possesses not only truth but supreme beauty.
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure.
In a completely rational society, the best of us would be teachers and the rest of us would have to settle for something else.
The mathematician's patterns, like the painter's or the poet's, must be beautiful.
In mathematics alone each generations adds a new story to the old structure.
In a completely rational society, the best of us would aspire to be teachers and the rest of us would have to settle for something less, because passing civilization along from one generation to the next ought to be the highest honor and the highest responsibility anyone could have.
The only way to learn mathematics is to do mathematics.
The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.
It is the supreme art of the teacher to awaken joy in creative expression and knowledge.
Education is what survives when what has been learned has been forgotten.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
A mathematician, like a painter or a poet, is a maker of patterns.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
The purpose of education is to replace an empty mind with an open one.
I hear and I forget. I see and I remember. I do and I understand.
or simply:
