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# Proof Theory

The development of proof theory can be naturally divided into: the prehistory of the notion of proof in ancient logic and mathematics; the discovery by Frege that mathematical proofs, and not only the propositions of mathematics, can (and should) be represented in a logical system; Hilbert's old axiomatic proof theory; Failure of the aims of Hilbert through Gödel's incompleteness theorems; Gentzen's creation of the two main types of logical systems of contemporary proof theory, natural deduction and sequent calculus (see the entry on automated reasoning); applications and extensions of natural deduction and sequent calculus, up to the computational interpretation of natural deduction and its connections with computer science. ... (See http://plato.stanford.edu )

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