“We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician". In practice he is apt to say: "try this; if it works that will justify it".” IfsMenWorldWantTryingRealDoneHandsRunningSchoolPracticeTheoryIdealsRelationMathematicsMathWhat You WantMathematicalConsistentJustifyReal WorldApplicationUsualMathematicianProbabilityParallels Author:John Edensor Littlewood
“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.” RealHandsScienceTimeUnderstandingTheoryDevelopmentToolsMathematicsMethodComplicatedMathInventionMathematicalCastingHand In Hand Author:David Hilbert
“There's a branch of math called the foundations of math. It's kind of like quantum mechanics. It's about how this very complex theory of math can be built up from very basic parts.” KindTheoryBuiltFoundationComplexesMathBranchesQuantumMechanicQuantum Mechanics Author:Tristan Perich
“It is well known that the man who first made public the theory of irrationals perished in a shipwreck in order that the inexpressible and unimaginable should ever remain veiled. And so the guilty man, who fortuitously touched on and revealed this aspect of living things, was taken to the place where he began and there is for ever beaten by the waves.” MenLifeShouldFirstsWellsMadeOrderKnownTakenHe ManTheoryAspectMathematicsGuiltWaveMathGuiltyMathematicalTouchedBeatenWell KnownLiving ThingsUnimaginableShipwreck Author:Proclus
“He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast.” KnowsLoveMayRealityPracticeSeaTheoryMathematicsCastsMathShipsMathematicalBoardsCompassSailorStatisticianSailing ShipsRuddersShips At SeaSailors And The SeaTheory And Practice Author:Leonardo da Vinci