# Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

… (Read on) from source :

https://www.quantamagazine.org/why-the-proof-of-fermats-last-theorem-doesnt-need-to-be-enhanced-via20190603/

Summary:

Andrew Wiles’ Proof of Fermat’s Last Theorem (FLT) by contradiction :

A. Assume FLT is true for all prime p (Why? sufficient to prove only for prime) such that:

$a^p + b^p = c^p$

B. then a, b, c could be rearranged into an Elliptic Curve,

C. then leverage such Elliptic Curve into a Galois Represebtation.

D. then a Modular Form.

E. then leads to an impossible weight 2 level 2 Modular Form.

Hence,

¬E -> ¬D -> ¬C -> ¬B -> ¬A (proved)

1950s Taniyama-Shimura-Weil proved the link below:

B -> (via assume C) -> D

Andrew Wiles’ took 7 years to complete the whole proof in 1994 by proving the missing link C -> D.