Common sense is the collection of prejudices acquired by age eighteen.
You know we all became mathematicians for the same reason: we were lazy.
Logic is invincible, because in order to combat logic it is necessary to use logic.
I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.
The highest form of pure thought is in mathematics.
It is not the job of mathematicians... to do correct arithmetical operations. It is the job of bank accountants.
Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.
It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.
The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed.
Poets do not go mad, but chess players do.
Do I contradict myself? Very well then, I can bear it.
The knowledge of which geometry aims is the knowledge of the eternal.
Every moment dies a man, Every moment one is born.
Logic is the art of going wrong with confidence.
An expert is someone who knows some of the worst mistakes that can be made in his subject and how to avoid them.
No, it is a very interesting number, it is the smallest number expressible as a sum of two cubes in two different ways.
In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it is the exact opposite.
Sir, I have found you an argument; but I am not obliged to find you an understanding.
The bitter and the sweet come from the outside, the hard from within, from one's own efforts.
The world needs heroes and it's better they be harmless men like me than villains like Hitler
The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics.
There is no national science, just as there is no national multiplication table; what is national is no longer science.
A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.
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