I didn't work especially hard at mathematics at school, because I knew that's what I'd be doing later. David Hilbert More Quotes by David Hilbert More Quotes From David Hilbert The arithmetical symbols are written diagrams and the geometrical figures are graphic formulas. David Hilbert diagramsfiguresmath Every kind of science, if it has only reached a certain degree of maturity, automatically becomes a part of mathematics. David Hilbert degreesmaturitykind Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. David Hilbert ontologyvitalityconnections An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us. David Hilbert perfecteasemen In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations. David Hilbert stresstwohands I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations. David Hilbert mathlongideas Geometry is the most complete science. David Hilbert geometryscience Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof. David Hilbert errorsmathbelieve Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical. David Hilbert disciplinethreedevelopment As long as a branch of science offers an abundance of problems, so long it is alive; a lack of problems foreshadows extinction or the cessation of independent development. David Hilbert independentdevelopmentlong Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. David Hilbert small-numbersprinciplessimple Is mathematics doomed to suffer the same fate as other sciences that have split into separate branches?... Mathematics is, in my opinion, an indivisible whole... May the new century bring with it ingenious champions and many zealous and enthusiastic disciples. David Hilbert championfatesuffering How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments. David Hilbert realmathtime Keep computations to the lowest level of the multiplication table. David Hilbert multiplicationlevelstables Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen. David Hilbert tombsknowsknowledge We ought not to believe those who today, adopting a philosophical air and with a tone of superiority, prophesy the decline of culter and are content with the unknowable in a self-satisfied way. For us there is no unknowable, and in my opinion there is also non whatsoever for the natural sciences. In place of this foolish unknowable, let our watchword on the contrary be: we must know - we shall know. David Hilbert philosophicalselfbelieve Before beginning [to try to prove Fermat's Last Theorem] I should have to put in three years of intensive study, and I haven't that much time to squander on a probable failure. David Hilbert should-havemathtime The tool which serves as intermediary between theory and practice, between thought and observation, is mathematics; it is mathematics which builds the linking bridges and gives the ever more reliable forms. David Hilbert bridgespracticegiving I do not see that the sex of the candidate is an argument against her admission as a Privatdozent. After all, the Senate is not a bathhouse. Objecting to sex discrimination being the reason for rejection of Emmy Noether's application to join the faculty at the University of Gottingen. David Hilbert discriminationrejectionsex Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of David Hilbert goalsecretlying
