Why hasn't Perfect Cuboid Problem been solved yet, whereas (possibly) more nontrivial ones such as FLT and Sphere packing have been solved?
I understand that calling some problems more nontrivial may be naive and seemingly trivial problems can be deceptively tricky, as with the FLT. All the same, FLT and to a lesser extent, Sphere Packing, garnered lots of attention by successive generations of mathematicians, until someone decided to finish it off and succeeded.
But, AFAIK, the Perfect Cuboid (PC) problem hasn't generated this kind of attention, perhaps because Fermat didn't leave a note about it. Is that the reason for PC remaining unsolved? One of the standard references for PC , Unsolved Problems in Number Theory , suggests several numerical results (p.178), but of course nothing like a proof, much like the status of FLT and Sphere Packing many decades ago.