[2608.15150] On the depth of Wiles's proof of Fermat's Last Theorem

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arXiv:2608.15150 (math)

[Submitted on 15 Aug 2026]

Title:On the depth of Wiles's proof of Fermat's Last Theorem

Authors:Yong Cheng, Colin McLarty<br>View a PDF of the paper titled On the depth of Wiles's proof of Fermat's Last Theorem, by Yong Cheng and Colin McLarty

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Abstract:What constitutes depth in a mathematical proof? This paper addresses this foundational question through a close case study of Andrew Wiles's proof of Fermat's Last Theorem. We propose a five-criteria framework: Difficulty, Originality, Fruitfulness, Unity, and Explanatory Power. By critically examining the limitations of each criterion and the intricate interrelations among them, we show that they do not merely coexist but capture genuinely complementary aspects of proof depth. Applying this framework to Wiles's proof, we then demonstrate that its celebrated depth does not reside in any single virtue, but rather emerges from a synthesis of all five criteria. Our analysis thus offers not only a novel lens for understanding Wiles's achievement, but also a flexible framework for evaluating depth across mathematical proofs more broadly.

Comments:<br>Accepted and to appear in Philosophia Mathematica

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History and Overview (math.HO)

Cite as:<br>arXiv:2608.15150 [math.HO]

(or<br>arXiv:2608.15150v1 [math.HO] for this version)

https://doi.org/10.48550/arXiv.2608.15150

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Yong Cheng [view email]<br>[v1]<br>Sat, 15 Aug 2026 10:03:34 UTC (24 KB)

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