It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed.
Henri PoincareA reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.
Henri PoincareThus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
Henri PoincareIt may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the later. Prediction becomes impossible, and we have the fortuitous phenomena.
Henri PoincareWhen the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it.
Henri Poincare