[Revised entry by Michael Rathjen and Wilfried Sieg on February 21, 2024.

Changes to: Main text, Bibliography, appendix-c.html, appendix-f.html, notes.html]

Proof theory is not an esoteric technical subject that was invented to support a formalist doctrine in the philosophy of mathematics; rather, it has been developed as an attempt to analyze aspects of mathematical experience and to isolate, possibly overcome, methodological problems in the foundations of mathematics. The origins of those problems, forcefully and sometimes contentiously formulated in the 1920s, are traceable to the transformation of mathematics in the nineteenth century: the emergence of abstract mathematics, its reliance on set…

Originally appeared on Stanford Encyclopedia of Philosophy Read More