TL;DR
Proof theory, originating in the 1920s as part of Hilbert's program, studies formal systems to understand the foundations of mathematics, with modern applications across mathematics, computer science, and philosophy.
Contribution
This paper provides an overview of proof theory's development and its significance in formalizing mathematical reasoning and foundations.
Findings
Proof theory links formal logic with foundational mathematics.
It has applications in computer science and philosophy.
The approach emphasizes precise linguistic and rule-based reasoning.
Abstract
Proof theory began in the 1920's as a part of Hilbert's program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted, finitary means. The program thus viewed mathematics as a system of reasoning with precise linguistic norms, governed by rules that can be described and studied in concrete terms. Today such a viewpoint has applications in mathematics, computer science, and the philosophy of mathematics.
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Taxonomy
TopicsHistory and Theory of Mathematics · Logic, programming, and type systems