It may happen that small differences in the initial conditions produce very great ones in the final phenomena. Henri Poincare More Quotes by Henri Poincare More Quotes From Henri Poincare A small error in the former will produce an enormous error in the latter. Henri Poincare latterproduceerrors Les faits ne parlent pas. Henri Poincare speakfacts Talk with M. Hermite. He never evokes a concrete image, yet you soon perceive that the more abstract entities are to him like living creatures. Henri Poincare abstractmathlife Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose. Henri Poincare powerfullawscience Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. Henri Poincare understoodknowsmean All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not. Henri Poincare freedomunderstandingscience Deviner avant de démontrer! Ai-je besoin de rappeler que c'est ainsi que se sont faites toutes les découvertes importantes. Henri Poincare science If we ought not to fear mortal truth, still less should we dread scientific truth. In the first place it can not conflict with ethics? But if science is feared, it is above all because it can give no happiness? Man, then, can not be happy through science but today he can much less be happy without it. Henri Poincare truthgivingmen Point set topology is a disease from which the human race will soon recover. Henri Poincare topologydiseaserace Science is facts just as houses are made of stones, so is science made of facts but a pile of stones is not a house and a collection of facts is not necessarily science. Henri Poincare Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does. Henri Poincare Mathematicians do not study objects, but relations between objects. Henri Poincare mathematiciansbetweenobjectsstudy To doubt everything, or, to believe everything, are two equally convenient solutions; both dispense with the necessity of reflection. Henri Poincare everythingreflectiondoubtbelieve How is an error possible in mathematics? Henri Poincare errorpossiblehowmathematics Science is built up of 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 Poincare morehousesciencefacts If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by the laws. Henri Poincare predictussaysituation
