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

[2608.15150] On the depth of Wiles's proof of Fermat's Last Theorem Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > History and Overview 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 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 View PDF HTML (experimental) 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: Accepted and to appear in Philosophia Mathematica Subjects: History and Overview (math.HO) Cite as: arXiv:2608.15150 [math.HO] (or arXiv:2608.15150v1 [math.HO] for this version) https://doi.org/10.48550/arXiv.2608.15150 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yong Cheng [ view email ] [v1] Sat, 15 Aug 2026 10:03:34 UTC (24 KB) Full-text links: Access Paper: 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 View PDF HTML (experimental) TeX Source view license Current browse context: math.HO < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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