Fermat's Last Theorem – The Proof (Wiles, 1995)¶
Overview
The centerpiece of this platform: Andrew Wiles' proof of Fermat's Last Theorem, presented step by step. From the Taniyama-Shimura Conjecture through Galois representations and deformation theory to the famous \(R = T\) theorem.
What Is This About?¶
In 1995, Andrew Wiles published a 109-page proof that resolved a 358-year-old conjecture. The central idea: show that every semistable elliptic curve is modular (a special case of the Taniyama-Shimura Conjecture). Together with Ribet's theorem, this implies that Fermat's Last Theorem is true.
The proof impressively connects number theory, algebraic geometry, and analysis – using tools that were only developed in the 20th century.
Articles in This Series¶
| # | Article | Topic |
|---|---|---|
| 1 | The Taniyama-Shimura Conjecture | Every elliptic curve is modular |
| 2 | Frey's Idea and Ribet's Theorem | TSC ⟹ FLT |
| 3 | Galois Representations | Elliptic curves as matrices |
| 4 | Deformation Theory | How to deform representations |
| 5 | \(R = T\) – The Heart of the Proof | Wiles' central theorem |
| 6 | The Taylor-Wiles Trick | The minimal case |
| 7 | The 3-5 Switch and the Conclusion | The finale |
| 8 | What Came After | Full TSC, Langlands program |
Recommended Order¶
The articles build strictly on each other and should be read in the order listed.
Prerequisites: Elementary Number Theory and Tools