“The mathematical fraternity is a little like a self-perpetuating priesthood. The mathematicians of today teach the mathematicians of tomorrow and, in effect, decide whom to admit to the priesthood.” LittlesSelfTodayTeachEffectsTomorrowMathematicalMathematicianPriesthoodFraternityPerpetuating Author:Paul Halmos
“To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.” BornAbilityTalentTasteMathematicsLuckInsightMathMathematicalConcentrationScholar Author:Paul Halmos
“Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.” TryingReasonScienceProveAccountsMathematicsErrorsMathListsTrialsExperimentsMathematicalMathematicianHypothesisTheoremsMath And ScienceTrial And ErrorMathematics And ScienceMathematics By MathematiciansFunny MathematicsLearning MathGuessworkMathematical ProofMaths Funny Author:Paul Halmos
“...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.” ScienceCasesSpecialExampleSourceConceptsEssenceMathematicsInstanceMathematicalConcreteGeneralities Author:Paul Halmos
“The only way to learn mathematics is to do mathematics.” WayLearningMathematicsMathMathematicalMathematicianAlgebraMath EducationLearning By DoingMathematics By MathematiciansLearning MathGreat MathMath LoveGood MathMath Is LikeMath ClassApplied Mathematics Author:Paul Halmos
“The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.” TruthJoySecretVisionLearningEnlightenmentMathematicsMathFormerMathematicalTensionEcstasyDiscoveringFlashEuphoria Author:Paul Halmos
“Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? ... Where does the proof use the hypothesis?” LooksDoeUseFightingAsksExampleMathematicsProofMathematicalHypothesisConversesMath EducationMathematical Proof Author:Paul Halmos
“Mathematics is not a deductive science - that's a cliché... What you do is trial and error, experimentation, guesswork.” MathematicsErrorsMathTrialsMathematicalMathematicianExperimentationTheoremsMath And ScienceTrial And ErrorMathematics And ScienceMathematics By MathematiciansFunny MathematicsLearning MathGuessworkMathematical ProofMaths Funny Author:Paul Halmos
“... the student skit at Christmas contained a plaintive line: "Give us Master's exams that our faculty can pass, or give us a faculty that can pass our Master's exams."” GivingLinesStudentsMastersMathematicsMathMathematicalFacultyExamSkit Author:Paul Halmos
“I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces."” FirstsLittlesRememberCertainSoundSpaceNumbersClassTheoryElementsPaperMathematicsAddSentencesMathCertaintyOccasionsMathematicalRangeAbstractContributionReviewsDomainPointlessAlgebraSeasoningValueless Author:Paul Halmos
