A correspondence problem for mathematical proof

Simon DeDeo; Eamon Duede

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arXiv · 2603.13680

A correspondence problem for mathematical proof

Simon DeDeo·Eamon Duede

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Abstract

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for a particular derivation to ''correspond'' to a particular proof. Mere existence of a formalization is not enough, and a substantive account of the required correspondence resolves into two criteria -- adequate representation (of the original theorem) and tracking (of the steps in the original proof). An examination of the actually-existing formalization systems we have today shows the variety of quasi-empirical ways we establish these criteria, and points towards new burdens that may be placed on the future evolution of mathematics itself.

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Simon DeDeo, Eamon Duede. 2026-03-14. A correspondence problem for mathematical proof. https://arxiv.org/abs/2603.13680

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