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RESEARCH PRODUCT
The forgotten mathematical legacy of Peano
Gabriele H. GrecoSzymon Doleckisubject
PeanoPeano's axioms of arithmeticPeano's counterexamplesWeierstrass maximum theoremabstract measuresGeneral MathematicsClosure (topology)tangencyinterioranti-distributive familiesfoundationdefinitions by abstractionlinear differential equationsaxiom of choiceLogical conjunctionPeano axiomsproofFormal languageAxiom of choiceMSC: Primary 01A55 01A6003-03 26-03 28-03 34-03 54-03; Secondary15A75 26A03 26A2426B25 26B05 28A1228A15 28A75.affine exterior algebra[MATH]Mathematics [math]reduction formulaeMathematicsnonlinear differential equationsoptimality conditionsdifferentiation of measuressweeping-tangent theoremPeano's axioms of geometryPeano's filling curvereduction of mathematics to setssurface areaclosuremean value theoremDirichlet functionNonlinear differential equationssubtangentsEpistemologymeasure theoryplanar measurelower and upper limits of setsdistributive familiescompactnessmathematical definitions1886 existence theoremdifferentiabilitydescription
International audience; The formulations that Peano gave to many mathematical notions at the end of the 19th century were so perfect and modern that they have become standard today. A formal language of logic that he created, enabled him to perceive mathematics with great precision and depth. He described mathematics axiomatically basing the reasoning exclusively on logical and set-theoretical primitive terms and properties, which was revolutionary at that time. Yet, numerous Peano’s contributions remain either unremembered or underestimated.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2019-02-01 | Dissertationes Mathematicae |