The forgotten mathematical legacy of Peano

Szymon Dolecki (1) , Gabriele Greco

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Peano; surface area; mean value theorem; Dirichlet function; Peano's counterexamples; Weierstrass maximum theorem; foundation; reduction of mathematics to sets; mathematical definitions; definitions by abstraction; axiom of choice; Peano's axioms of arithmetic; Peano's axioms of geometry; affine exterior algebra; reduction formulae; differentiability; lower and upper limits of sets; tangency; optimality conditions; linear differential equations; nonlinear differential equations; Peano's filling curve; interior; closure; distributive families; anti-distributive families; compactness; planar measure; measure theory; abstract measures; differentiation of measures; sweeping-tangent theorem; 1886 existence theorem; proof; subtangents

Domaines: Mathématiques [math]

Szymon Dolecki, Gabriele Greco. The forgotten mathematical legacy of Peano. Dissertationes Mathematicae, 2019, 537, pp.1-77. ⟨10.4064/dm769-4-2018⟩. ⟨hal-02174864⟩