Proof mining

Proof mining

In proof theory (a branch of mathematical logic), proof mining is a research program [cite book
title = Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
author = Ulrich Kohlenbach
publisher = Springer Verlag, Berlin
year = 2008
pages = 1–536
] that analyzes formalized proofs, especially in analysis, to obtain explicit bounds 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

* Ulrich Kohlenbach and Paulo Oliva, "Proof Mining: A systematic way of analysing proofs in mathematics", "Proc. Steklov Inst. Math", 242:136–164, 2003

* Paulo Oliva, "Proof Mining in Subsystems of Analysis", BRICS PhD thesis [http://citeseer.ist.psu.edu/oliva03proof.html citeseer]


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