A small error in the former will produce an enormous error in the latter. Henri Poincare More Quotes by Henri Poincare More Quotes From Henri Poincare One does not ask whether a scientific theory is true, but only whether it is convenient. Henri Poincare convenient theory doe To invent is to discern, to choose. Henri Poincare Geometry is not true, it is advantageous. Henri Poincare mathematical truth science The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain. Henri Poincare eye science past Mathematics is the art of giving the same name to different things. Henri Poincare math science art 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 observation experience science It is not order only, but unexpected order, that has value. Henri Poincare values unexpected order Ideas rose in clouds; I felt them collide until pairs interlocked, so to speak, making a stable combination. Henri Poincare business clouds ideas But for harmony beautiful to contemplate, science would not be worth following. Henri Poincare beautiful beauty art 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 mathematics chance simple 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 nature work math 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 independent science reality Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered. Henri Poincare generations disease math When the logician has resolved each demonstration into a host of elementary operations, all of them correct, he will not yet be in possession of the whole reality, that indefinable something that constitutes the unity ... Now pure logic cannot give us this view of the whole; it is to intuition that we must look for it. Henri Poincare views giving reality What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? Henri Poincare idaho feelings giving Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence.... The two propositions: "The earth turns round" and "it is more convenient to suppose the earth turns round" have the same meaning; there is nothing more in the one than in the other. Henri Poincare math two moving A 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 ontology mind people [T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous. Henri Poincare different ambition math 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 history children moving Need we add that mathematicians themselves are not infallible? Henri Poincare mathematician add needs
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