Women have a passion for mathematics. They divide their age in half, double the price of their clothes, and always add at least five years to the age of their best friend.

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.

Physical reality does not require that we be pleased with its mechanism; we must see the implications of a theory for what they are and not for what we would like them to be.

Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.

It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

…numerical precision is the very soul of science, and its attainment affords the best, perhaps the only criterion of the truth of theories and the correctness of experiments.

She would not have cared to confess how infinitely she preferred the exactitude, the star-like impersonality, of figures to the confusion, agitation, and vagueness of the finest prose.

One must divide one's time between politics and equations. But our equations are much more important to me, because politics is for the present, while our equations are for eternity.

As the several items can be exchanged, they must be equal; but in what terms? Not in pounds, yards, or hours; they are equal in value. Then what is wanted is a unit of value to reckon by.

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.

It appears that the solution of the problem of time and space is reserved to philosophers who, like Leibniz, are mathematicians, or to mathematicians who, like Einstein, are philosophers.

A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

Life is a linear equation in which you can't cross multiply! If you think you can do it, you can do it. If you think you can't do it, you can't do it. It's a simple formula!

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.[Statement of the second law of thermodynamics, 1862]