Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means.
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 Poincare. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.
Henri PoincareIt may happen that small differences in the initial conditions produce very great ones in the final phenomena.
Henri PoincareDoubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.
Henri PoincareWhat is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
Henri Poincare