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Henri Poincare Quotes

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Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection  (Henri Poincare Quotes) What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?  (Henri Poincare Quotes) It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details  (Henri Poincare Quotes) In the old days when people invented a new function they had something useful in mind  (Henri Poincare Quotes) If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing  (Henri Poincare Quotes) A scientist worthy of his name, about all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature  (Henri Poincare Quotes) In one word, to draw the rule from experience, one must generalize; this is a necessity that imposes itself on the most circumspect observer  (Henri Poincare Quotes) 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 Quotes) If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of the same universe at a succeeding moment  (Henri Poincare Quotes) If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living  (Henri Poincare Quotes) One does not ask whether a scientific theory is true, but only whether it is convenient  (Henri Poincare Quotes) Pure logic could never lead us to anything but tautologies; it can create nothing new; not from it alone can any science issue  (Henri Poincare Quotes) The subliminal self is in no way inferior to the conscious self. It knows how to choose and to divine  (Henri Poincare Quotes) Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don’t change. Matter is not important, only form interests them  (Henri Poincare Quotes) One would have to have completely forgotten the history of science so as to not remember that the desire to know nature has had the most constant and the happiest influence on the development of mathematics  (Henri Poincare Quotes) It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed  (Henri Poincare Quotes) The task of the educator is to make the child’s spirit pass again where its forefathers have gone, moving rapidly through certain stages but suppressing none of them. In this regard, the history of science must be our guide  (Henri Poincare Quotes) ... the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know  (Henri Poincare Quotes) Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be  (Henri Poincare Quotes) When the physicists ask us for the solution of a problem, it is not drudgery that they impose on us, on the contrary, it is us who owe them thanks  (Henri Poincare Quotes) ... 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 Poincare Quotes) A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us  (Henri Poincare Quotes) Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work  (Henri Poincare Quotes) Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house  (Henri Poincare Quotes) The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another  (Henri Poincare Quotes) 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  (Henri Poincare Quotes) Mathematicians do not deal in objects, but in relations between objects; thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only  (Henri Poincare Quotes) Doubting everything and believing everything are two equally convenient solutions that guard us from having to think  (Henri Poincare Quotes) If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science  (Henri Poincare Quotes) Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose  (Henri Poincare Quotes)
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