Accepted proofs: Objective truth, or culturally robust?

Andrew Granville

Accepted proofs: Objective truth, or culturally robust?

Abstract

How does the mathematical community accept that a given proof is correct? Is objective verification based on explicit axioms feasible, or must the reviewer's experiences and prejudices necessarily come into play? Can automated provers avoid mistakes (as well as experiences and prejudices) to provide objective verification? And can an automated prover's claims be provably verified? We will follow examples of proofs that were found to be flawed, but then corrected (as the proof plan was sufficiently robust), as well as accepted "proofs" that turned out to be fundamentally wrong. What does this imply about the desirability of the current community standard for proofs? We will discuss whether mathematical culture is unavoidably part of the acceptance of a proof, no matter how much we try to develop foolproof, objective "proof systems".

Keywords mathematical proof objectivity mathematical practice epistemology of mathematics

Cite this article

Granville, A. (2023). Accepted proofs: Objective truth, or culturally robust?. M×Φ — Annals of Mathematics and Philosophy, 1(2), 25–90.

Granville, Andrew. “Accepted proofs: Objective truth, or culturally robust?.” M×Φ — Annals of Mathematics and Philosophy 1, no. 2 (2023): 25–90.

Granville, Andrew. “Accepted proofs: Objective truth, or culturally robust?.” M×Φ — Annals of Mathematics and Philosophy, vol. 1, no. 2, 2023, pp. 25–90.

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  title = {{Accepted proofs: Objective truth, or culturally robust?}},
  author = {Andrew Granville},
  journal = {M×Φ — Annals of Mathematics and Philosophy},
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  number = {2},
  pages = {25--90},
  year = {2023},
  issn = {3038-6381},
  language = {en},
  keywords = {mathematical proof, objectivity, mathematical practice, epistemology of mathematics},
  url = {https://www.mxphi.com/all-issues/volume-i-number-2-2023/accepted-proofs-objective-truth/},
  note = {License: CC BY-ND 4.0},
}

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