I am unsure of whether it is normal, but to me, intuitively Fermats last theorem should not hold.
If anyone intuitively believed it to be correct, why?
Can someone explain so I understand somewhat why FLT holds without reading a massive and complex proof?
You will find a lot of intuitive reasons why Fermat last theorem holds in the following book : "Modular Forms and Fermat’s Last Theorem", from Cornell, Silverman and Joseph, I quite liked it in my young years.