… (Read on) from source :

** 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:

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.**