Who answers for a proof? What the person who presents it commits to, even once it is verified

Public note written in response to Terence Tao's essay "Mathematics in the age of AI" (arXiv:2608.16753, based on his ICM 2026 public lecture). Submitted to the communal blog Proofs and Prompts on 26 October 2026 and deposited here unchanged. Tao proposes that a result should not be published unless its authors can give a clear, correct and properly attributed expert-level talk on it, even if the proof has been formally verified. The note asks what that rule leaves open: what the person who presents a result commits to, and to whom they are answerable, once formal correctness is already established. It carries over to mathematics the three conditions of accountability developed in Checa Prieto and Fernández Tamames, "Why AI Cannot Sign" (Law, Innovation and Technology, forthcoming 2027): having been able to refrain, giving reasons for the particular case, and having something to lose. It argues that the canon is a chain of attributable acts rather than an authored whole, and that the relevant line runs not between proofs made with or without AI, but between results someone answers for and results no one answers for. This is an initial intervention; a longer article developing the analysis is in preparation.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24144541
Primary Topic
History and Theory of Mathematics
Type
article
Field-Weighted Citation Impact
0.00
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article

Who answers for a proof? What the person who presents it commits to, even once it is verified

Jose Fernández Tamames
Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
article

Who answers for a proof? What the person who presents it commits to, even once it is verified

Jose Fernández Tamames
article en

Abstract

Public note written in response to Terence Tao's essay "Mathematics in the age of AI" (arXiv:2608.16753, based on his ICM 2026 public lecture). Submitted to the communal blog Proofs and Prompts on 26 October 2026 and deposited here unchanged. Tao proposes that a result should not be published unless its authors can give a clear, correct and properly attributed expert-level talk on it, even if the proof has been formally verified. The note asks what that rule leaves open: what the person who presents a result commits to, and to whom they are answerable, once formal correctness is already established. It carries over to mathematics the three conditions of accountability developed in Checa Prieto and Fernández Tamames, "Why AI Cannot Sign" (Law, Innovation and Technology, forthcoming 2027): having been able to refrain, giving reasons for the particular case, and having something to lose. It argues that the canon is a chain of attributable acts rather than an authored whole, and that the relevant line runs not between proofs made with or without AI, but between results someone answers for and results no one answers for. This is an initial intervention; a longer article developing the analysis is in preparation.

Zenodo (CERN European Organization for Nuclear Research)
UNIE Universidad (ES)
History and Theory of Mathematics
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