“For most people, the major hurdle in grasping modern insights into the nature of the universe is that these developments are usually phrased using mathematics.” PeopleUniverseModernDevelopmentMajorsMathematicsInsightGraspingHurdle Author:Brian Greene
“Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists.” TypeDevelopmentMathematicsHistoricalAncientDetailsObscureSpecialists Author:Ivor Grattan-Guinness
“Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.” TypeDevelopmentMathematicsReasoningSignificanceFormal Author:Alfred North Whitehead
“The subject for which I am asking your attention deals with the foundations of mathematics. To understand the development of the opposing theories existing in this field one must first gain a clear understnding of the concept "science"; for it is as a part of science that mathematics originally took its place in human thought.” FirstsHumansDealsAttentionClearSubjectsFieldsTheoryDevelopmentConceptsGainsAskingMathematicsFoundationOpposingHuman Thought Author:L. E. J. Brouwer
“The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.” WellsKnownGreaterDevelopmentProveMathematicsWell KnownPrecisionTheoremsIntegers Book:Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 Source: Kurt Gödel: Collected Works: Volume I: Publications 1929-1936
“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