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AnnalesMathematicaeSilesianae26(2012),7-23
PraceNaukoweUniwersytetuŚląskiegonr3031,Katowice
DESCRIPTIONOFMATHEMATICS.
DESCRIPTIONINMATHEMATICS.
MATHEMATICSASAWAYOFDESCRIBING1
ANdRzEjPELCzaR
AnnualLecturededicatedtothememoryofProfessorAndrzejLasota
1.Descriptionofmathematics
A.Whenaskedaboutthenatureofmathematics,probablythesimplest(and,
likely,mostfrequent)answerwewouldgiveisthatmathematicsisadeductive
science.Onecan(or,perhaps,oneshould?)agreewiththat.Butwealso
oughttonotice,thatthedevelopmentofmathematicsispurelyinductive.
Wheneverweconsideratheory,withwell-foundedaxiomsandprimitive
notions,weneverdevelopsuchatheorybylistingallcorrectsentenceswithin
thistheoryandthenverifyingwhethertheyarecorrectornot(thatis,we
neverconsiderallcorrectlystatedconjecturesandcheckwhethertheyare
theorems).HCandidatesfortheorems”arepickedaccordingtoanHinformal”
key(i.e.tryingtogeneralizesomealreadyknowntheorems,captureanalo-
giesbetweenresultsfromothertheories,seekanswerstoquestionsposedby
physics,biology,socialsciencesetc.byfirstformulatingappropriatemath-
ematicalmodels,andthen–withinsuchmodels–consideringconceivable
theoremsthatwouldprovideanswerstotheoriginalquestions).
Received:5.10.2012.
1TranslatedfromPolishtoEnglishbyPawełGładki.
