New Concepts of Formal Proof and Proof Representations

The notion of proof is the most important concept of mathematics: mathematics is the science of propositions, which cannot be directly understood as true, but whose truth can be established by a cognitive tool: the proof. The mathematical proof obtained its modern form quite recently by David Hilbert. The modern proofs are stepwise derivations of the result. In this joint project of the Vienna University of Technology and the Steklov Mathematical Institute of the Russian Academy of Sciences more general concepts of proof should be developed, e.g. circular proofs for induction or non-well founded proofs which are nevertheless sound. The overall aim of the project is to extend the realm of mathematics by further developing its most important tool: the proof.

The notion of proof is the most important concept of mathematics: mathematics is the science of propositions, which cannot be directly understood as true, but whose truth can be established by a cognitive tool: the proof. The mathematical proof obtained its modern form quite recently by David Hilbert. The modern proofs are stepwise derivations of the result. In this joint project of the Vienna University of Technology and the Steklov Mathematical Institute of the Russian Academy of Sciences more general concepts of proof should be developed, e.g. circular proofs for induction or non-well founded proofs which are nevertheless sound. The overall aim of the project is to extend the realm of mathematics by further developing its most important tool: the proof.