Editing Proof theory (section)

==Formal and informal proof==<!-- This section is linked from [[Black–Scholes]] and [[Mathematical proof]]-->
{{Main |Formal proof}}

The ''informal'' proofs of everyday mathematical practice are unlike the ''formal'' proofs of proof theory. They are rather like high-level sketches that would allow an expert to reconstruct a formal proof at least in principle, given enough time and patience. For most mathematicians, writing a fully formal proof is too pedantic and long-winded to be in common use.

Formal proofs are constructed with the help of computers in [[interactive theorem proving]]. 
Significantly, these proofs can be checked automatically, also by computer. Checking formal proofs is usually simple, whereas ''finding'' proofs ([[automated theorem proving]]) is generally hard. An informal proof in the mathematics literature, by contrast, requires weeks of [[peer review]] to be checked, and may still contain errors.