Are there thoughtfully simple concepts that we cannot currently prove? I was driving and just happened to wonder if there existed some concepts that are simple to grasp, yet are not provable via current mathematical techniques. Does anyone know of concepts that fit this criteria?
I imagine the level of simple could vary considerably from person to person, myself being on the very low end of things.

we know that $e$ is transcendental, $\pi$ is transcendental.  but still we dont know that whether  $e + \pi$  and $e - \pi$ is transcendental or not. we know that atleast one of them is transcendental which follows from simple calculation.
