| _version_ | 1866901690844708864 |
|---|---|
| author | ACOSTA PADILLA, ALFREDO LUIS |
| author_facet | ACOSTA PADILLA, ALFREDO LUIS |
| contents | <p>Andrew Wiles' 1995 proof of Fermat's Last Theorem, while celebrated as one of mathematics' greatest achievements, operates entirely within the real-complex analytic framework (ℝ/ℂ)—a structure we have previously demonstrated to be algebraically incomplete due to dimensional collapse in the Cantor-Dedekind construction of 1872.</p> <p>This paper demonstrates that Wiles' proof, far from establishing FLT in fundamental algebraic reality, merely demonstrates a contradiction within the projected shadow-world of ℝ/ℂ. His essential reliance on modular forms as holomorphic functions on ℂ, elliptic curves embedded in ℂ, p-adic completions, and topological methods all inherit the fundamental incompleteness of ℝ.</p> <p>We show that:<br>(1) The Frey curve construction assumes solutions live in ℚ when they require extensions W/ℚ<br>(2) Modularity is an analytic artifact of working in ℂ, not an algebraic necessity <br>(3) A direct 10-page proof in the Rational Worlds framework renders Wiles' 150-page argument obsolete<br>(4) Wiles proved "no contradiction exists in ℝ/ℂ projection," not "FLT is true in algebraic reality"</p> <p>If the ontological framework is incorrect, the proof is false—regardless of technical correctness within that framework. This is analogous to Ptolemaic astronomy: mathematically consistent but ontologically wrong.</p> <p>The paper includes:<br>- Rigorous demonstration that Wiles' proof depends essentially on ℝ/ℂ<br>- Analysis of how dimensional collapse invalidates his argument<br>- Complete 10-page algebraic proof of FLT via Rational Worlds<br>- Comparison: Wiles (150 pages, ℝ/ℂ) vs. Rational Worlds (10 pages, W/ℚ)</p> <p>This work builds on our previous demonstration that ℝ is not a "completion" of ℚ but rather a dimensional collapse that destroys algebraic structure (Zenodo, 2025).</p> <p>Supplementary materials:<br>- "The Algebraic Incompleteness of the Real Numbers: Why Cantor and Dedekind Were Wrong" (Zenodo DOI: [previous paper])<br>- "Fermat's Last Theorem via Dimensional Collapse: The Rectangles Proof" (10-page algebraic proof)</p> <p>Mathematical community challenge: Refute our demonstration of ℝ's incompleteness in one page, or accept its consequences for Wiles' proof. There is no third option.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17849665 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Incompleteness of Wiles' Proof: Why Fermat's Last Theorem Remains Unproven in Fundamental Algebraic Reality ACOSTA PADILLA, ALFREDO LUIS Fermat's Last Theorem, Andrew Wiles, Foundations of Mathematics, Real Numbers, Algebraic Completeness, Cantor-Dedekind Construction, Rational Worlds, Modular Forms, Elliptic Curves, Number Theory, Mathematical Ontology, Dimensional Collapse, Field Extensions, Alternative Proof, Mathematical Foundations, Galois Theory, p-adic Numbers, Complex Analysis, Philosophy of Mathematics <p>Andrew Wiles' 1995 proof of Fermat's Last Theorem, while celebrated as one of mathematics' greatest achievements, operates entirely within the real-complex analytic framework (ℝ/ℂ)—a structure we have previously demonstrated to be algebraically incomplete due to dimensional collapse in the Cantor-Dedekind construction of 1872.</p> <p>This paper demonstrates that Wiles' proof, far from establishing FLT in fundamental algebraic reality, merely demonstrates a contradiction within the projected shadow-world of ℝ/ℂ. His essential reliance on modular forms as holomorphic functions on ℂ, elliptic curves embedded in ℂ, p-adic completions, and topological methods all inherit the fundamental incompleteness of ℝ.</p> <p>We show that:<br>(1) The Frey curve construction assumes solutions live in ℚ when they require extensions W/ℚ<br>(2) Modularity is an analytic artifact of working in ℂ, not an algebraic necessity <br>(3) A direct 10-page proof in the Rational Worlds framework renders Wiles' 150-page argument obsolete<br>(4) Wiles proved "no contradiction exists in ℝ/ℂ projection," not "FLT is true in algebraic reality"</p> <p>If the ontological framework is incorrect, the proof is false—regardless of technical correctness within that framework. This is analogous to Ptolemaic astronomy: mathematically consistent but ontologically wrong.</p> <p>The paper includes:<br>- Rigorous demonstration that Wiles' proof depends essentially on ℝ/ℂ<br>- Analysis of how dimensional collapse invalidates his argument<br>- Complete 10-page algebraic proof of FLT via Rational Worlds<br>- Comparison: Wiles (150 pages, ℝ/ℂ) vs. Rational Worlds (10 pages, W/ℚ)</p> <p>This work builds on our previous demonstration that ℝ is not a "completion" of ℚ but rather a dimensional collapse that destroys algebraic structure (Zenodo, 2025).</p> <p>Supplementary materials:<br>- "The Algebraic Incompleteness of the Real Numbers: Why Cantor and Dedekind Were Wrong" (Zenodo DOI: [previous paper])<br>- "Fermat's Last Theorem via Dimensional Collapse: The Rectangles Proof" (10-page algebraic proof)</p> <p>Mathematical community challenge: Refute our demonstration of ℝ's incompleteness in one page, or accept its consequences for Wiles' proof. There is no third option.</p> |
| title | The Incompleteness of Wiles' Proof: Why Fermat's Last Theorem Remains Unproven in Fundamental Algebraic Reality |
| topic | Fermat's Last Theorem, Andrew Wiles, Foundations of Mathematics, Real Numbers, Algebraic Completeness, Cantor-Dedekind Construction, Rational Worlds, Modular Forms, Elliptic Curves, Number Theory, Mathematical Ontology, Dimensional Collapse, Field Extensions, Alternative Proof, Mathematical Foundations, Galois Theory, p-adic Numbers, Complex Analysis, Philosophy of Mathematics |
| url | https://doi.org/10.5281/zenodo.17849665 |