We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.
Nobody listens to mathematicians
—Carl Sagan in Cosmos
The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics.
—Oliver Wendell Holmes Jr.
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.
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.
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.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture.
Mathematics is the queen of the sciences.
—Carl Friedrich Gauss
I went off to college planning to major in math or philosophy-- of course, both those ideas are really the same idea.
In mathematics you don't understand things. You just get used to them.
—Johann von Neumann
I have hardly ever known a mathematician who was capable of reasoning.
Proof is the idol before whom the pure mathematician tortures himself.
—Sir Arthur Eddington
The mathematics is not there till we put it there.
We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.