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 How is error possible in mathematics? Henri Poincare mathematical mathematics errors Experiment is the sole source of truth. Henri Poincare experiments sole source The mind uses its faculty for creativity only when experience forces it to do so. Henri Poincare creativity mind math Mathematical discoveries, small or great are never born of spontaneous generation. Henri Poincare generations spontaneity discovery 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 philosophical nature science Mathematicians do not study objects, but the relations between objects. Henri Poincare mathematician study relation It is by logic we prove. It is by intuition we discover. Henri Poincare truth science knowledge So is not mathematical analysis then not just a vain game of the mind? To the physicist it can only give a convenient language; but isn't that a mediocre service, which after all we could have done without; and, it is not even to be feared that this artificial language be a veil, interposed between reality and the physicist's eye? Far from that, without this language most of the initimate analogies of things would forever have remained unknown to us; and we would never have had knowledge of the internal harmony of the world, which is, as we shall see, the only true objective reality. Henri Poincare eye science reality 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 logic issues science In the old days when people invented a new function they had something useful in mind. Henri Poincare function mind people The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp. Henri Poincare nature beautiful life All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance. Henri Poincare progress together two The aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relation between things. Henri Poincare simplicity imagination science All that is not thought is pure nothingness; since we can think only thoughts, and all the words we use to speak of things can express only thoughts, to say there is something other than thought is therefore an affirmation which can have no meaning. Henri Poincare affirmation use thinking Astronomy is useful because it raises us above ourselves; it is useful because it is grand; .... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony. Henri Poincare body mind men Guessing before proving! Need I remind you that it is so that all important discoveries have been made? Henri Poincare important discovery science ...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 math feelings numbers 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 form relation long 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 development desire remember A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations. Henri Poincare logical guilty mind
