Metamathematics (nonfiction)

The title page of the Principia Mathematica (shortened version, including sections only up to *56), an important work of metamathematics.

Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories.

Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59).

An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.

Fiction cross-references

• Gnomon Algorithm
• Mathematics

Nonfiction cross-reference

• Algorithm (nonfiction)
• David Hilbert (nonfiction)
• Logic (nonfiction)
• Mathematics (nonfiction)
• Bertrand Russell (nonfiction)
• Alfred North Whitehead (nonfiction)

External links:

• Metamathematics @ Wikipedia