“The scientist has to take 95 per cent of his subject on trust. He has to because he can't possibly do all the experiments, therefore he has to take on trust the experiments all his colleagues and predecessors have done. Whereas a mathematician doesn't have to take anything on trust. Any theorem that's proved, he doesn't believe it, really, until he goes through the proof himself, and therefore he knows his whole subject from scratch. He's absolutely 100 per cent certain of it. And that gives him an extraordinary conviction of certainty, and an arrogance that scientists don't have.” KnowsGivingBelieveDoneWholeScienceCertainBeliefSubjectsScientistExtraordinaryConvictionProofExperimentsCertaintyArroganceCentsMathematicianColleaguesScratchesPredecessorsTheorems Author:Christopher Zeeman
“I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.” MeanTwoWholeHalfDoubtImpossibleEqualMathematicsMathProofLawyerMathematicalProgrammingMathematicianMathematical Proof Author:Carl Friedrich Gauss
“On the whole, however, the conclusions I have drawn from the proofs quoted may, I believe, safely be relied on. Assuredly they will not be disturbed either by the lays of a poet displaying the exaggeration of his craft, or by the compositions of the chroniclers that are attractive at truth's expense; the subjects they treat of being out of the reach of evidence, and time having robbed most of them of historical value by enthroning them in the region of legend.” BelieveMayWholeValuesI BelieveSubjectsPoetEvidenceTreatsLaysHistoricalProofConclusionCraftsAttractiveRegionsExpensesLegendsCompositionDisturbedExaggerationHistorical Value Book:History of Greece Source: History of Greece
“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.” MayWholeHandsRealityUsedNumbersCasesConceptsConsequenceBasesProofDistinctionNeglectQuantityEntityPropositionsAxioms Author:Georg Cantor