As many of you know, Dr. Andrew Wiles proved the theorem a number of years back after working on it at Princeton for about 7 years. My kashya was that clearly this is not the proof Fermat had in mind. Wiles proof is about 250 pages long, I believe, and goes off into areas of math that may not have even been around at the time of Fermat.
We still need a simple and direct proof of the straightforward statement of the theorem that anybody can understand. I have done some work, but am not sure if this is a good forum to share.