It is a well-known experience that the only truly enjoyable and profitable way of studying mathematics is the method of "filling in details" by one's own efforts.
The laws of nature are written by the hand of God in the language of mathematics.
Chaotic mathematics is essentially the study of chaos. It can't be chaos, if you can study it and it has an order.
A chemist who does not know mathematics is seriously handicapped.
Here is something Category-Theorists like: it is trivial, but not trivially trivial.
The abstract analysis of the world by mathematics and physics rests on the concepts of space and time.
I believe there are 15, 747, 724, 136, 275, 002, 577, 605, 653, 961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185, 631, 031, 296 protons in the universe and the same number of electrons.
The only way to learn mathematics is to do mathematics.
It saddens me that educated people don't even know that my subject exists.
Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
Mathematics is universal. It's discovered by human beings, but the rules of mathematics are the same throughout the universe and the laws of the universe.
All mathematics is tautology.
The art of doing mathematics consists in finding that special case which contains all the germs of generality
In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.
When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.
If you learn music, you'll learn history. If you learn music, you'll learn mathematics. If you learn music, you'll learn most all there is to learn.
Physics without mathematics is meaningless.
The only reason psychology students don't have to do more and harder mathematics than physics students is because the mathematicians haven't yet discovered ways of dealing with problems as hard as those in psychology.
Football is not played on paper, it is played on a pitch. This game is not mathematics and in football, two plus two very rarely equals four - it's usually three or five.
Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course. There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.