Mathematics is a game played according to certain simple rules with meaningless marks on paper.
Biographical history, as taught in our public schools, is still largely a history of boneheads; ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant general the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.
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.
Mathematical Mark all mathematical heads, which be only and wholly bent to those sciences, how solitary they be themselves, how unfit to live with others, and how unapt to serve in the world.
[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.
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.
The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal.
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.
Poets do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom. I am not, as will be seen, in any sense attacking logic: I only say that this danger does lie in logic, not in imagination.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
What is this frog and mouse battle among the mathematicians?
Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
Mathematics is concerned with "all possible worlds."
Mathematics is no more computation than typing is literature.
The mathematician has reached the highest rung on the ladder of human thought.
Mathematics is not only real, but it is the only reality.
Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only.
It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
Mathematics is as much an aspect of culture as it is a collection of algorithms.
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
Mathematics is the supreme judge; from its decisions there is no appeal.
You know we all became mathematicians for the same reason: we were lazy.
[Mathematics] is an independent world created out of pure intelligence.
It would be better for the true physics if there were no mathematicians on earth.
Mathematics, in the common lay view, is a static discipline based on formulas...But outside the public view, mathematics continues to grow at a rapid rate...the guid to this growth is not calculation and formulas, but an open ended search for pattern.
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