Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical. David Hilbert More Quotes by David Hilbert More Quotes From David Hilbert Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. David Hilbert race math country Sometimes it happens that a man's circle of horizon becomes smaller and smaller, and as the radius approaches zero it concentrates on one point. And then that becomes his point of view. David Hilbert sad zero men Some people have got a mental horizon of radius zero and call it their point of view. David Hilbert zero views people Mathematics is a game played according to certain simple rules with meaningless marks on paper. David Hilbert simple games math If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven? David Hilbert awakening would-be years Begin with the simplest examples. David Hilbert simplest example For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: "We must know - we will know!" David Hilbert knows science knowledge Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs. David Hilbert consistency intuition understanding No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. David Hilbert men ideas needs If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology. David Hilbert astrology stupid men A mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution. David Hilbert effort successful order The art of doing mathematics consists in finding that special case which contains all the germs of generality. David Hilbert special math art One must be able to say at all times--instead of points, straight lines, and planes--tables, chairs, and beer mugs David Hilbert lines tables beer He who seeks for methods without having a definite problem in mind seeks in the most part in vain. David Hilbert problem mind science Physics is becoming too difficult for the physicists. David Hilbert difficult becoming physics Galileo was no idiot. Only an idiot could believe that science requires martyrdom - that may be necessary in religion, but in time a scientific result will establish itself. David Hilbert math time believe The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science. David Hilbert doe math science I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek. David Hilbert confused games mean One hears a lot of talk about the hostility between scientists and engineers. I don't believe in any such thing. In fact I am quite certain it is untrue... There cannot possibly be anything in it because neither side has anything to do with the other. David Hilbert science believe facts However unapproachable these problems may seem to us and however helpless we stand before them, we have, nevertheless, the firm conviction that their solution must follow by a finite number of purely logical processes. David Hilbert finite-number may numbers
