“...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
“A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept,and when I want to learn something new, I make it my first job to build one.” WantFirstsJobsUnderstandingEducationExampleConceptsMathematicsMathSomething NewStatisticsIndispensableThoroughLearning MathGood MathThorough Understanding Author:Paul Halmos
“The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases.” HeartProblemBigsCasesSpecialExampleTheoryMathematicsProfoundInsightConcrete Book:Selecta: expository writing Source: Selecta: expository writing
“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
