Mathematics and Plausible Reasoning：Vol. II: Patterns of Plausible Inference

Thisisaguidetothepracticalartofplausiblereasoning,particularlyinmathematicsbutalsoineveryfieldofhumanactivity.Usingmathematicsastheexampleparexcellence,ProfessorPolyashowshoweventhatmostrigorousdeductivedisciplineisheavilydependentontechniquesofguessing,inductivereasoning,andreasoningbyanalogy.Insolvingaproblem,theanswermustbeguessedatbeforeaproofcanevenbegin,andguessesareusuallymadefromaknowledgeoffacts,experience,andhunches.Thetrulycreativemathematicianmustbeagoodguesserfirstandagoodproverafterward;manyimportanttheoremshavebeenguessedbutnotproveduntilmuchlater.Inthesameway,solutionstoproblemscanbeguessed,andagoodguesserismuchmorelikelytofindacorrectsolution.Thisworkmighthavebeencalled"HowtoBecomeaGoodGuesser."ProfessorPolya'sdeepunderstandingofthepsychologyofcreativemathematicsenableshimtoshowthereaderhowtoattackanewproblem,howtogetattheheartofit,whattrainsofthoughtmayleadtoasolution.Thereisnomagicformulahere,butthereismuchpracticalwisdom.VolumesIandIItogethermakeacoherentworkonMathematicsandPlausibleReasoning.VolumeIonInductionandAnalogystandsbyitselfasanessentialbookforanyoneinterestedinmathematicalreasoning.VolumeIIonPatternsofPlausibleInferencebuildsontheexamplesofVolumeIbutisnototherwisedependentonit.AmoresophisticatedreaderwithsomemathematicalexperiencewillhavenodifficultyinreadingVolumeIIindependently,thoughhewillprobablywanttoreadVolumeIafterward.ProfessorPolya'searliermoreelementarybookHowtoSolveItwascloselyrelatedtoMathematicsandPlausibleReasoningandfurnishedsomebackgroundforit.