Quendi it was my friend who really piqued my interest in FLT. After I graduated college, I took a podunk job just to get to the big city. Met a coworker Engineer and we quickly became friends. Turns out he was an Ex-JW who got DF'd and left because his newborn needed a blood transfusion. How strange is that?
Anyway, I'm astounded at the classical mathematical works he has read since then, and he has helped educate me a lot on the history of mathematics. We both switched jobs but get together every few weeks and work on mathematics and physics problems ranging from FLT to reconciling the Theory of Relativiy with Quantum Physics, to Green Energy.
He encouraged me to look at FLT, so I did and came up with that solution domain, and we have done some interesting things. I'm hesitant to say more simply because I have yet to find anyone else who has tried our path to a solution. Like I said, the odds are low simply because of how many people have tried to solve this before, but it's fun to try, and we've noticed/learned some very interesting things that may provide a path towards a solution without resorting to "new math".