One thing that makes it an appealing problem to solve is its apparent simplicity. It’s almost embarrassing that our modern mathematical technology isn’t adequat

One thing that makes it an appealing problem to solve is its apparent simplicity. It’s almost embarrassing that our modern mathematical technology isn’t adequate to resolve such an elementary question. …or maybe the fact that it proves so hard to answer shows that we’re just wrong for thinking that it’s ‘elementary’. Therefore, any solution would necessarily require new breakthroughs that would lead to greater general understanding. So: 1) mathematicians would like to save face 2) you can’t solve difficult problems without accidentally solving other difficult ones that turn out to have immediate ‘practical’ importance