Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.
Henri PoincareEinstein does not remain attached to the classical principles, and when presented with a problem in physics he quickly envisages all of its possibilities. This leads immediately in his mind to the prediction of new phenomena which may one day be verified by experiment.
Henri PoincareI then began to study arithmetical questions without any great apparent result, and without suspecting that they could have the least connexion with my previous researches. Disgusted at my want of success, I went away to spend a few days at the seaside, and thought of entirely different things. One day, as I was walking on the cliff, the idea came to me, again with the same characteristics of conciseness, suddenness, and immediate certainty, that arithmetical transformations of indefinite ternary quadratic forms are identical with those of non-Euclidian geometry.
Henri Poincare[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.
Henri PoincareA first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?
Henri Poincare