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I'm looking for something that dives into the philosophical idea of a "proof," and explains how the subjects of mathematics and logic deal with it. Does anyone have any book or article recommendations that might lead me to the discussion I am looking for?
Any information you can offer would be greatly appreciated!
Thurston, W. P. (1995). On proof and progress in mathematics. For the learning of mathematics, 15(1), 29-37.
Gold, B., & Simons, R. A. (Eds.). (2008). Proof and other dilemmas: Mathematics and philosophy (Vol. 59). MAA.
Krantz, S. G. (2011). The proof is in the pudding: The changing nature of mathematical proof. Springer Science & Business Media.
Detlefsen, M. (Ed.). (2005). Proof and knowledge in mathematics. Routledge.
Detlefsen, M. (Ed.). (2005). Proof, logic and formalization. Routledge.
Davis and Hersh's The Mathematical Experience is an excellent read and gives an excellent introduction to the philosophy of mathematics.
