The thing is though that MANY bugs slip through even the most thorough code reviews. As a security researcher, I can tell you there is literally no system out there that doesn't have such a bug in it.
The systems we deal with in software are massive compared with your typical mathematical framework though. But FLT is probably on similar scope.
It takes thorough review by advanced mathematicians to verify correctness.
This is not unlike a code review.
Most people vastly underestimate how complex and esoteric modern research mathematics are.