The forgotten mathematical legacy of Peano
| Affiliation auteurs | Affiliation ok |
| Titre | The forgotten mathematical legacy of Peano |
| Type de publication | Journal Article |
| Year of Publication | 2019 |
| Auteurs | Dolecki S, Greco GH |
| Journal | DISSERTATIONES MATHEMATICAE |
| Pagination | 1-77 |
| Type of Article | Article |
| ISSN | 0012-3862 |
| Mots-clés | abstract measures, affine exterior algebra, anti-distributive families, axiom of choice, closure, compactness, definitions by abstraction, differentiability, differentiation of measures, Dirichlet function, distributive families, foundation, Interior, linear differential equations, lower and upper limits of sets, mathematical definitions, mean value theorem, measure theory, nonlinear differential equations, optimality conditions, Peano, Peano's axioms of arithmetic, Peano's axioms of geometry, Peano's counterexamples, Peano's filling curve, planar measure, reduction formulae, reduction of mathematics to sets, Surface area, sweeping-tangent theorem, tangency, Weierstrass maximum theorem |
| Résumé | 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. |
| DOI | 10.4064/dm769-4-2018 |