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Like the crest of a peacock so is mathematics at the head of all knowledge.
The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful.
For the things of this world cannot be made known without a knowledge of mathematics.
It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
It is the merest truism, evident at once to unsophisticated observation, that mathematics is a human invention.
I advise my students to listen carefully the moment they decide to take no more mathematics courses. They might be able to hear the sound of closing doors. Everybody a mathematician?
As for everything else, so for a mathematical theory: beauty can be perceived but not explained.
Between the penis and the mathematical one . . . there exists nothing. Nothing! It is a vacuum.
To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls.
One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.
Mathematics is the only instructional material that can be presented in an entirely undogmatic way.
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 assure you that mine are greater.
How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?