This mystery can be solved, but in order for this to be solved there can be only two possibilities that I can come up with. One, the thieves come forward and tell the museum were the painting are, or two someone finds the painting somewhere and recognizes it's the painings stolen from the museum. If those two things don't happen, then no it can't be solved. The reason behind this is because without a actual suspect, it can be almost impossible to find the paintings. It's been decades that the paints were missing so, the theives are probably dead so that's a problem, and so the paintings can probably be hidden or destroyed.