"DAVID HILBERT EST SURTOUT CONNU POUR LE << FORMALISME >> ET LA METHODE AXIOMATIQUE QU'IL A INTRODUITS DANS LES MATHEMATIQUES. UNE CONSEQUENCE DES TRAVAUX HILBERTIENS, MOINS CONNUE, ET QUE CE TRAVAIL SE PROPOSE D'EXAMINER, EST LA TRANSFORMATION DE LA NOTION D'EXISTENCE EN MATHEMATIQUE. DES PREMIERS TRAVAUX MATHEMATIQUES DE HILBERT, EN THEORIE DES INVARIANTS, JUSQU'A SA THEORIE DE LA DEMONSTRATION, NOUS MONTRONS COMMENT S'ELABORE UNE CONCEPTION NOUVELLE DE L'EXISTENCE MATHEMATIQUE, ET COMMENT CETTE CONCEPTION SE DEMARQUE DES CONCEPTIONS CONSTRUCTIVES, USUELLES A LA FIN DU XIXE SIECLE. DANS CE PARCOURS, L'AXIOMATISATION DE LA GEOMETRIE EUCLIDIENNE APPARAIT COMME LE MOMENT CRUCIAL OU SE MET EN PLACE LA CONCEPTION DE L'EXISTENCE COMME NONCONTRADICTION. LA FORMALISATION CROISSANTE DU TRAVAIL DE HILBERT A PARTIR DE SES PREMIERS COURS DE GEOMETRIE, ET LE LENT RETRAIT DE L'INTUITION SENSIBLE QUI S'EN SUIT CONDUISENT LE MATHEMATICIEN A DONNER UN STATUT INEDIT AUX OBJETS GEOMETRIQUES. IL APPARAIT TOUTEFOIS QUE LA VISEE DE HILBERT N'EST PAS UNE RUPTURE TOTALE AVEC L'INTUITION, NI L'OBTENTION D'UNE THEORIE RADICALEMENT ABSTRAITE. LES FONDEMENTS DE L'ARITHMETIQUE, DONT L'ENJEU EST LA JUSTIFICATION DE L'EXISTENCE DE L'ENSEMBLE DES NOMBRES REELS, CONSTITUENT UNE AUTRE ETAPE IMPORTANTE DANS L'ELABORATION DE LA NOTION D'EXISTENCE DES OBJETS MATHEMATIQUES. LA PREUVE DE NONCONTRADICTION DE L'ARITHMETIQUE, SUR LAQUELLE REPOSE L'EXISTENCE DE L'INFINI, S'AVERE CEPENDANT PLUS DIFFICILE QUE NE L'AVAIT PENSE HILBERT DANS UN PREMIER TEMPS, ET CETTE DIFFICULTE CONDUIT LE MATHEMATICIEN A ELABORER SA THEORIE DE LA DEMONSTRATION. L'INFINI MATHEMATIQUE N'Y EST ENTENDU NI COMME EXISTANT REELLEMENT, NI COMME PURE FICTION, MAIS EST COMPARE AUX IDEAUX KANTIENS. PAR CE STATUT DONNE A L'INFINI ET, PLUS GENERALEMENT, A LA PLUPART DES OBJETS MATHEMATIQUES, HILBERT NOUS PARAIT FINALEMENT FONDER LA CONCEPTION MODERNE DE CES OBJETS."
This is a placeholder reference for a Event entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Event entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Place entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Existence (philosophie) Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Mathématiques Fondements Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Philosophie Allemagne Mathématiques 19e siècle Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Philosophie Allemagne Mathématiques 20e siècle Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Preuve, Théorie de la Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
Théorèmes d'existence Thèses et écrits académiques.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.