# Definition:Proof Theory

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## Definition

**Proof theory** is the subfield of mathematical logic which studies proofs as mathematical objects, thus allowing them to be analysed mathematically.

## Also see

- Results about
**proof theory**can be found**here**.

## Historical Note

The mathematical branch known as **Proof theory** was initiated by David Hilbert in his attempt to prove the consistency of mathematics.

His approach was later developed by Gerhard Karl Erich Gentzen, who developed a complete system for the treatment of the subject.

## Sources

- 1987: Gaisi Takeuti:
*Proof Theory*(2nd ed.) ... (next): Introduction - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**proof theory (metalogic, metamathematics, logical syntax)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**proof theory (metalogic, metamathematics, logical syntax)**