All of mathematics is a tale about groups. Henri Poincare More Quotes by Henri Poincare More Quotes From Henri Poincare 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 intuition logic math Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection. Henri Poincare reflection science believe The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. Henri Poincare math beautiful science It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all. Henri Poincare men science ideas 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 important teaching long Geometry is the art of correct reasoning from incorrectly drawn figures. Henri Poincare figures math art It is far better to foresee even without certainty than not to foresee at all. Henri Poincare foreseeing absolute-certainty certainty Every good mathematician should also be a good chess player and vice versa. Henri Poincare vices player science 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 nature knowing beautiful One geometry cannot be more true than another; it can only be more convenient. Henri Poincare convenient geometry mathematics There are no solved problems; there are only problems that are more or less solved. Henri Poincare ontology math knowledge Intuition is more important to discovery than logic. Henri Poincare intuition important discovery Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty. Henri Poincare teaching truth science Analyse data just so far as to obtain simplicity and no further. Henri Poincare data simplicity 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 passion party mean It is through science that we prove, but through intuition that we discover. Henri Poincare intuition creativity science Mathematics is the art of giving the same name to different things. Henri Poincare names math art Mathematicians are born, not made. Henri Poincare born made math Tolstoi explains somewhere in his writings why, in his opinion, “Science for Science's sake” is an absurd conception. We cannot know all the facts, since they are practically infinite in number. We must make a selection. Is it not better to be guided by utility, by our practical, and more especially our moral, necessities? Henri Poincare writing numbers science How is error possible in mathematics? Henri Poincare mathematical mathematics errors
