Wiles' Proof of Fermat's Last Theorem via Modularity — E8 Intelligence Research

FINDING: Fermat's Last Theorem (FLT) states no positive integers a,b,c satisfy aⁿ+bⁿ=cⁿ for n>2; proven by Wiles (1994) via modularity of elliptic curves. | MATH: aⁿ + bⁿ = cⁿ has no solutions in ℤ⁺ for n ≥ 3. Wiles–Taylor proof: every semistable elliptic curve over ℚ is modular (Taniyama–Shimura–Weil conjecture). Frey curve: y² = x(x−aⁿ)(x+bⁿ) for a hypothetical solution is semistable and non-modular — contradiction. | CONNECTION: The n=2 case a²+b²=c² generates Pythagorean triples via the unit circle parametrization; the rational points on x²+y²=1 form a group isomorphic to rotations, connecting to the circle group U(1) and the golden-ratio-adjacent Fibonacci triples (3,4,5), (5,12,13), (8,15,17) — consecutive Fibonacci numbers generate Pythagorean triples: (Fₙ₋₁Fₙ₊₁, 2FₙFₙ₊₁, Fₙ₋₁Fₙ₊₁+2Fₙ²) where the hypotenuse/leg ratio → √5 ≈ 2.236, and φ = (1+√5)/2 = 1.618... emerges from the Fibonacci structure underlying these triples. | DEPTH: 9 FINDING: The proof of FLT is a corollary of the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com