C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.
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It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.
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Part II. Ch. 2 : Mathematical Definitions and Education, p. 129Henri Poincare
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Toute définition implique un axiome, puisqu'elle affirme l'existence de l'objet défini. La définition ne sera donc justifiée, au point de vue purement logique, que quand on aura démontré qu'elle n'entraîne pas de contradiction, ni dans les termes, ni avec les vérités antérieurement admises.
Henri Poincare
Il a inventé l'histoire.
Marie Anne de Vichy-Chamrond
Many people think that the progress of the human race is based on experiences of an empirical, critical nature, but I say that true knowledge is to be had only through a philosophy of deduction. For it is intuition that improves the world, not just following a trodden path of thought. Intuition makes us look at unrelated facts and then think about them until they can all be brought under one law. To look for related facts means holding onto what one has instead of searching for new facts. Intuition is the father of new knowledge, while empiricism is nothing but an accumulation of old knowledge. Intuition, not intellect, is the 'open sesame' of yourself.
Albert Einstein
Indeed, it is not intellect, but intuition which advances humanity. Intuition tells man his purpose in this life.
Albert Einstein
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
Alan Turing
Poincare, Henri
Poinsot, Louis
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