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41 " The American public is therefore much better prepared than has been thought for investigating the origin of the notion of space. "
― Henri Poincaré ,
42 " O societate este cu atât mai înaintată, cu cât are mai mare grijă faţă de bufonii ei. "
― Henri Poincaré
43 " When we say force is the cause of motion, we are talking metaphysics; and this definition, if we had to be content with it, would be absolutely fruitless, would lead to absolutely nothing. "
― Henri Poincaré , Science and Hypothesis
44 " It's through science that we prove, but through intuition that we discover. "
45 " La recherche de la vérité doit être le but de notre activité ; c'est la seule fin qui soit digne d'elle. Sans doute nous devons d'abord nous efforcer de soulager les souffrances humaines, mais pourquoi ? "
― Henri Poincaré , The Value of Science: Essential Writings of Henri Poincare
46 " Cependant quelquefois la vérité nous effraye. "
47 " Only Science and Art make civilization worth-while. One may be startled by the formula: Science for the sake of Science; and yet, it is worth as much as Life for Life's sake, if life is but misery; and even as Happiness for Happiness' sake, unless one believes that all pleasures are the same in quality, unless one is ready to admit that the goal of civilization is to furnish alcohol to all who love to drink.All actions have goals. We must suffer, we must work, we must pay for our seats at the show. But, we pay that we may see, or that, at least, others may see some day. "
48 " For fifteen days I strove to prove that there could not be any functions like those I have since called Fuchsian functions. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours. "
49 " The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle. Are we then to admit that the enunciations of all the theorems with which so many volumes are filled, are only indirect ways of saying that A is A? "
50 " El hombre de ciencia no estudia la naturaleza porque sea útil; la estudia porque encuentra placer, y encuentra placer porque es bella. Si la naturaleza no fuera bella, no valdría la pena conocerla, ni valdría la pena vivir la vida. No hablo aquí, entendámoslo bien, de esta belleza que impresiona los sentidos, de la belleza de las cualidades y de las apariencias; no es que la desdeñe, lejos de ahí, pero no tiene nada que ver con la ciencia. Quiero hablar de esa belleza, más íntima, que proviene del orden armonioso de las partes y que sólo una inteligencia pura puede comprender. Por así decirlo es ella la que da un cuerpo, un esqueleto a las halagadoras apariencias que embellecen nuestros sentidos, y sin este soporte, la belleza de estos sueños fugitivos sería imperfecta, porque sería indecisa y huiría siempre "
51 " The very possibility of mathematical science seems an insoluble contradiction. If this science is deductive in appearance only, from where does it get its perfect rigor that no one dares to doubt? If, on the contrary, all the propositions it sets forth can be derived from one another by the rules of formal logic, why is mathematics not reducible to an immense tautology? Syllogism can teach us nothing that is essentially new and, if everything originated in the principle of identity, it should also be possible to reduce everything to it. Are we then to concede that the statements of all those theorems filling so many volumes are merely roundabout ways of saying that A is A? "
