“Every mathematical discipline goes through three periods of development: the naive, the formal, and the critical.” ThreeDevelopmentDisciplinePeriodsCriticalMathematicalFormalNaive Author:David Hilbert
“The most powerful influence exercised by the Arabs on general natural physics was that directed to the advances of chemistry ; a science for which this race created a new era.(...) Besides making laudatory mention of that which we owe to the natural science of the Arabs in both the terrestrial and celestial spheres, we must likewise allude to their contributions in separate paths of intellectual development to the general mass of mathematical science.” NaturalPowerfulRacePathInfluenceDevelopmentMassIntellectualPhysicsMathematicalErasContributionMost PowerfulChemistrySpheresCelestialNatural ScienceNew EraIntellectual Development Author:Alexander von Humboldt
“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 our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?” FactsSpiritLyingNextGoalSecretBehindsRichGenerationsCenturyFieldsParticularDevelopmentMethodStriveCastsWideGladMathematicalLiftsGlancesVeils Author:David Hilbert
“I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to the point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.” PeopleThinkingTogetherCertainIndividualPathSubjectsFieldsParticularDevelopmentCivilizationMathematicsIndependentBoundsMathematicalInevitableTerritoryTheorems Author:William Thurston
“Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.” DoneStoriesProblemMightSchoolHumanityWealthExistenceEducationTeachingStudentsMastersDevelopmentConflictConceptsMathematicsFundamentalsHistoricalSeriesMathTechniqueMathematicalUnnecessaryTopicsPointingExplainingTextbooksExamUnsolved Problems Author:Ian Stewart
“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
“It is with children that we have the best chance of studying the development of logical knowledge, mathematical knowledge, physical knowledge, and so forth.” InspirationalChildrenChanceEducationStudyPsychologyDevelopmentMathematicalLogicalEpistemologyChild Development Book:Dialogue with Jean Piaget Source: Dialogue with Jean Piaget
“As a graduate student, I wrote a long paper connecting the dots between mathematical models of learning and language development in children. It was published in a major journal.” ChildrenLongLanguageStudentsDevelopmentPaperMajorsModelsMathematicalGraduatesJournalConnectingDotsGraduate StudentsConnecting The DotsMathematical ModelsLanguage Development Author:Steven Pinker