The introduction of numbers as coordinates by reference to the particular division scheme of the open one-dimensional continuum is an act of violence whose only practical vindication is the special calculatory manageability of the ordinary number continuum with its four basic operations.
To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.
Proof is an idol before which the mathematician tortures himself.
A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.
You know we all became mathematicians for the same reason: we were lazy.
A mathematician's reputation rests on the number of bad proofs he has given.
What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?
Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
Mechanics is the paradise of the mathematical sciences because by means of it one comes to the fruits of mathematics.
I am too good for philosophy and not good enough for physics. Mathematics is in between.
The Mandelbrot set is the most complex mathematical object known to mankind.
"The most powerful single idea in mathematics is the notion of a variable."
All the mathematical sciences are founded on relations between physical laws and laws of numbers.
Algebra is generous; she often gives more than is asked of her.
Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another.
Wherever there is a number, there is beauty.
The mathematician's patterns, like the painter's or the poet's, must be beautiful.
The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.
The study of mathematics is apt to commence in disappointment.
Pure mathematics is, in its way, the poetry of logical ideas.
The life of a mathematician is dominated by an insatiable curiosity, a desire bordering on passion to solve the problems he is studying.
Physics is to mathematics what sex is to masturbation.
A good mathematical joke is better, and better mathematics, than a dozen mediocre papers.
Mathematics are well and good but Nature keeps dragging us around by the nose.
Well done is better than well said.
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