500+ Sourced quotes
In pure mathematics the maximum of detachment appears to be reached: the mind moves in an infinitely complicated pattern, which is absolutely free from temporal considerations. Yet this very freedom - the essential condition of the mathematician's activity - perhaps gives him an unfair advantage. He can only be wrong - he cannot cheat.
Mathematics may be legitimately pursued for its own sake or for the sake of its applications or with a view to understanding its logical foundations and internal structure or in the interest of magnanimity or for the sake of its bearings upon the supreme concerns of man as man or from two or more of these motives combined.
The real object of true naturalists, in Sir W. Thomson's meaning of the word, when they employ mathematics to assist them, is not to make mathematical exercises (though that may be necessary), but to find out the connections of known phenomena, and by deductive reasoning, to obtain a knowledge of hitherto unknown phenomena.
I disagree with Adler, who wrote (in the New Yorker) that there is no point in being a mathematician unless you can be a great mathematician. That's nonsense. Mathematics is like a Gothic cathedral. If you can build a little part of it, it is there - forever - in some sense. At least I have the illusion that it is so.