Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of studying the objects of a particular mathematical theory, it examines the mathematical theories as such, especially with respect to their logical structure. It concentrates mainly on the way in which theorems are derived from axioms.

# Proof Theory

## See also

Logic, Mathematics, Metatheorem, Proof
*Portions of this entry contributed by Margherita
Barile*

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## References

Birkhoff, G. and Mac Lane, S.*A Survey of Modern Algebra, 5th ed.*New York: Macmillan, p. 326, 1996.Chaitin, G. J.

*The Unknowable.*New York: Springer-Verlag, 1999.Hofstadter, D. R.

*Gödel, Escher, Bach: An Eternal Golden Braid.*New York: Vintage Books, p. 23, 1989.

## Referenced on Wolfram|Alpha

Proof Theory## Cite this as:

Barile, Margherita and Weisstein, Eric W. "Proof Theory." From *MathWorld*--A Wolfram
Web Resource. https://mathworld.wolfram.com/ProofTheory.html