Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.
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.
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.
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.
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.
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.
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.
[A mathematician is a] scientist who can figure out anything except such simple things as squaring the circle and trisecting an angle.
What is this frog and mouse battle among the mathematicians?
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.
Mathematics is concerned with "all possible worlds."
Mathematics is no more computation than typing is literature.
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.
It would be better for the true physics if there were no mathematicians on earth.
[Mathematics] is an independent world created out of pure intelligence.
You know we all became mathematicians for the same reason: we were lazy.
It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.
Mathematics is the handwriting on the human consciousness of the very Spirit of Life itself.
Mathematics is not only real, but it is the only reality.
Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.
The mathematician has reached the highest rung on the ladder of human thought.
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.
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