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 More Quotes by Henri Poincare More Quotes From Henri Poincare A cat is witty, he has nerve, he knows how to do precisely the right thing at the right moment. Henri Poincare nerves cat witty Mathematical discoveries, small or great are never born of spontaneous generation They always presuppose a soil seeded with preliminary knowledge and well prepared by labour, both conscious and subconscious. Henri Poincare preparation math discovery Science is built up with 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 stones house science It may happen that small differences in the initial conditions produce very great ones in the final phenomena. Henri Poincare finals differences science Chance ... must be something more than the name we give to our ignorance. Henri Poincare ignorance names science We also know how cruel the truth often is, and we wonder whether delusion is not more consoling. Henri Poincare often-is truth wonder Most striking at first is the appearance of sudden illumination, a manifest sign of long unconscious prior work. Henri Poincare illumination long firsts Thought is only a flash between two long nights, but this flash is everything. Henri Poincare night science thinking How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education. Henri Poincare skeletons understanding science 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 unity giving order I entered an omnibus to go to some place or other. At that moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with non-Euclidean geometry. Henri Poincare feet steps ideas Doubting everything and believing everything are two equally convenient solutions that guard us from having to think Henri Poincare spiritual believe thinking Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose. Henri Poincare purpose half littles What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils. Henri Poincare definitions understanding science For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold. Henri Poincare science long ideas It is with logic that one proves; it is with intuition that one invents. Henri Poincare prove-it intuition logic Sociology is the science with the greatest number of methods and the least results. Henri Poincare technology numbers science 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 thanks problem science Just as houses are made of stones, so is science made of facts. Henri Poincare stones house facts One does not ask whether a scientific theory is true, but only whether it is convenient. Henri Poincare convenient theory doe
