Cogito ergo sum brings us a very interesting problem. Rene Descartes posited this "I think therefore I am" idea which popularized metaphysical solipsism - the idea that no reality can exist outside of your mind or your mental state. As per his notion, you cannot prove to me that you exist, I can only know that I exist, because I experience myself existing. This statement is problematic and thus seen as sophomoric because it is untestable.
However, before discarding it, I'd like to extend it a little bit by delving into the realm of the hypothetical. In a hypothetical world where metaphysical solipsism could be true, it could be either one of two values - true or false. If it is false, and therefore impossible, there is nothing further to discuss. If on the other hand, it is indeed possible, then let's imagine that it is the case. I, the self, am the only thing that exists and everything else is an extension of my mind, or rather a representation of it. What happens when I die? Can I die? How could I possibly know that I've died and would the ceasing of experience signify my death (and thus the death of all existence) or would my death cause my experience of the world to cease?
I don't think those are questions that can ever be answered concretely, but there is another more pertinent question back in the converse. In the hypothetical world where solipsism is false, but in the mind of an actor, he absolutely believes it to be true, is there any way to prove to him beyond a doubt that his theory of solipsism is crazy? If you, as a devout solipsist, die and go to heaven (assuming heaven and God exist), and you see God, and he greets you but instead of reciprocating the greeting, you charge him with your idea of disbelief, how could he prove to you that he's real? The God problem here is that to the ultimate skeptic that is face to face with this God, there is no way to absolutely convince him that the current situation is reality.
In fact, even beyond the skeptical solipsist, even if you just take an extreme skeptic, how can he be convinced that he's in heaven and not in some long-winded dream? Sticking with Descartes' original summary, the only thing you can be certain of is your existence, and everything else including experience, logic and knowledge can be false. This means that solipsism could be self-defeating in that your logic of your solipsist-driven world view could be false or illogical. Again this doesn't prove that solipsism is impossible, only that it could be impossible under certain circumstances, but it does leave open the possibility that you could one day face a God only to doubt his very existence, should you be religiously inclined. However even if you don't believe in solipsism, you could still be the ultimate skeptic.