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.
Henri PoincarePure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue.
Henri PoincareTolstoi explains somewhere in his writings why, in his opinion, โScience for Science's sakeโ is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities?
Henri Poincare