de Mathématiques de Luminy
From the why to the how: proof theory from 1950 to date.
Du pourquoi au comment : la théorie de la démonstration de 1950 à nos jours.
The author presents the evolution of Proof Theory during the second
halfof the 20th century. His introduction replaces in their historical
context the works of Goedel, Herbrand and Gentzen as well as the constructivist
tradition (Brouwer's intuitions), the introduction by Church, Curry
and Kleene of the lambda-calculus and the pivotal role played by Keisel.
By stressing thepermanent interactions between the theoretic and algorithmic
aspects, his text describes side by side the "why" - what
is, the fundamentalist aspect - and the "how" - that is the
pragmatic aspect - of Proof Theory.
Keywords : Proving; Contemporary Mathematics.