Formorethantwothousandyearsafamiliaritywithmathematicshasbeenregardedasanindispensablepartoftheintellectualequipmentofeveryculturedperson.Today,unfortunately,thetraditionalplaceofmathematicsineducationisingravedanger.Theteachingandlearningofmathematicshasdegeneratedintotherealmofrotememorization,theoutcomeofwhichleadstosatisfactoryformalabilitybutdoesnotleadtorealunderstandingortogreaterintellectualindependence.ThisneweditionofRichardCourant’sandHerbertRobbins’sclassicworkseekstoaddressthisproblem.Itsgoalistoputthemeaningbackintomathematics.Writtenforbeginnersandscholars,forstudentsandteachers,forphilosophersandengineers,WhatisMathematics?,SecondEditionisasparklingcollectionofmathematicalgemsthatoffersanentertainingandaccessibleportraitofthemathematicalworld.Coveringeverythingfromnaturalnumbersandthenumbersystemtogeometricalconstructionsandprojectivegeometry,fromtopologyandcalculustomattersofprincipleandtheContinuumHypothesis,thisfascinatingsurveyallowsreaderstodelveintomathematicsasanorganicwholeratherthananemptydrillinproblemsolving.Withchapterslargelyindependentofoneanotherandsectionsthatleadupwardfrombasictomoreadvanceddiscussions,readerscaneasilypickandchooseareasofparticularinterestwithoutimpairingtheirunderstandingofsubsequentparts.BroughtuptodatewithanewchapterbyIanStewart,WhatisMathematics?,SecondEditionoffersnewinsightsintorecentmathematicaldevelopmentsanddescribesproofsoftheFour-ColorTheoremandFermat’sLastTheorem,problemsthatwerestillopenwhenCourantandRobbinswrotethismasterpiece,butonesthathavesincebeensolved.Formalmathematicsislikespellingandgrammar--amatterofthecorrectapplicationoflocalrules.Meaningfulmathematicsislikejournalism--ittellsaninterestingstory.Butunlikesomejournalism,thestoryhastobetrue.Thebestmathematicsislikeliterature--itbringsastorytolifebeforeyoureyesandinvolvesyouinit,intellectuallyandemotionally.WhatisMathematicsislikeafinepieceofliterature--itopensawindowontotheworldofmathematicsforanyoneinterestedtoview.
