You might not understand all the details of the paper, but you can definitely follow the thrust of the argument and see the elegance in it without advanced math skills.
The really hard part (and main part of Wile's contribution to the proof) was proving something called the Taniyama–Shimura–Weil conjecture. However if you skip that bit and just accept that the conjecture is true the rest of the steps of the proof are both elegant and relatively easy to follow (if you gloss over some of the details) for anybody with a decent grasp of basic math.
The book Fermat's Last Theorem by Simon Singh is a pretty great read and does a good job of outlining the basic structure of the proof for anybody with a decent grasp of high school mat.
The really hard part (and main part of Wile's contribution to the proof) was proving something called the Taniyama–Shimura–Weil conjecture. However if you skip that bit and just accept that the conjecture is true the rest of the steps of the proof are both elegant and relatively easy to follow (if you gloss over some of the details) for anybody with a decent grasp of basic math.
The book Fermat's Last Theorem by Simon Singh is a pretty great read and does a good job of outlining the basic structure of the proof for anybody with a decent grasp of high school mat.