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.
The Mandelbrot set is the most complex mathematical object known to mankind.
It is not the job of mathematicians... to do correct arithmetical operations. It is the job of bank accountants.
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.
It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know.
Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes.
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.
The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
I'm very good at integral and differential calculus, I know the scientific names of beings animalculous; In short, in matters vegetable, animal, and mineral, I am the very model of a modern Major-General.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty-a beauty cold and austere ... yet sublimely pure and capable of stern perfection such as only the greatest art can show.
The principle is so perfectly general that no particular application of it is possible.
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.
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.
A book on the new physics, if not purely descriptive of experimental work, must essentially be mathematical.
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.
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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