proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four correspo ...

, a branch of

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

, proof mining (or proof unwinding) is a research program that studies or analyzes formalized proofs, especially in

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, to obtain explicit bounds,

ranges In the Hebrew Bible and in the Old Testament, the word ranges has two very different meanings. Leviticus In Leviticus 11:35, ranges probably means a cooking furnace for two or more pots, as the Hebrew word here is in the dual number; or perhaps ...

or rates of convergence from proofs that, when expressed in natural language, appear to be nonconstructive. This research has led to improved results in analysis obtained from the analysis of classical proofs.

References

Further reading