Four Colors Suffice How the Map Problem Was Sol

OnOctober23，1852，ProfessorAugustusDeMorganwrotealettertoacolleague，unawarethathewaslaunchingoneofthemostfamousmathematicalconundrumsinhistory--onethatwouldconfoundthousandsofpuzzlersformorethanacentury.Thisistheamazingstoryofhowthe"mapproblem"wassolved.Theproblemposedinthelettercamefromaformerstudent：Whatistheleastpossiblenumberofcolorsneededtofillinanymap(realorinvented)sothatneighboringcountiesarealwayscoloreddifferently?Thisdeceptivelysimplequestionwasofminimalinteresttocartographers，whosawlittleneedtolimithowmanycolorstheyused.Buttheproblemsetoffafrenzyamongprofessionalmathematiciansandamateurproblemsolvers，amongthemLewisCarroll，anastronomer，abotanist，anobsessivegolfer，theBishopofLondon，amanwhosethiswatchonlyonceayear，aCaliforniatrafficcop，andabridegroomwhospenthishoneymooncoloringmaps.Intheirpursuitofthesolution，mathematicianspaintedmapsondoughnutsandhorseshoesandplayedwithpatternedsoccerballsandthegreatrhombicuboctahedron.Itwouldbemorethanonehundredyears(andcountlesscoloredmaps)laterbeforetheresultwasfinallyestablished.Eventhen，difficultquestionsremained，andtheintricatesolution--whichinvolvednofewerthan1，200hoursofcomputertime--wasgreetedwithasmuchdismayasenthusiasm.Providingaclearandelegantexplanationoftheproblemandtheproof，RobinWilsontellshowaseeminglyinnocuousquestionbaffledgreatmindsandstimulatedexcitingmathematicswithfar-flungapplications.Thisistheentertainingstoryofthosewhofailedtoprove，andthosewhoultimatelydidprove，thatfourcolorsdoindeedsufficetocoloranymap.Thisneweditionfeaturesmanycolorillustrations.ItalsoincludesanewforewordbyIanStewartontheimportanceofthemapproblemandhowitwassolved.