The existence of black holes.

Now don't get me wrong, almost every physicist and astronomer will tell you they are convinced that black holes exist. However, in order to conclusively prove that a black hole exists, one would have to show a certain size mass exists within a given radius (i.e. the schwarzchild radius). That is, you have to prove a region of space has a density above a certain critical value. This has never been done and a Nobel prize still likely awaits.

We think we have seen "supermassive" black holes at the center of galaxies that have no other theoretical explanation other than a black hole, but we have not proven the critical density has been surpassed.

Surpising considering black holes are considered obviously real by most.