Plutarch 
Profession: philosopher.
Henri Poincaré Profession: mathematician.
A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
Mathematical discoveries, small or great, are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious.
Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long as the relations don't change. Matter is not important, only form interests them.
Mathematics is the art of giving the same name to different things.
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. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
To force the future of mathematics the true method is to study its history and its present state.
What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.
George Polya Profession: mathematician.
Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps, no more ideas than the inexperienced, but appreciates more what he has and uses it better.
The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.
The open secret of real success is to throw your whole personality at a problem.
Matthew Prior Would give a man excessive trouble.
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