Thanks. I've written on agnosticism below.
The question of "proof," I think, is a red herring since that's a standard in math and language games, not philosophy, and the question of whether God exists is mainly philosophical. Richard Dawkins addressed this point when he interpreted the question of theism as a matter of probability. The question is whether God's existence is likely or unlikely, not whether we can be 100% certain one way or the other since we have such certainty about hardly anything (as Descartes showed with his skepticism; mind you, Descartes the mathematician also introduced the red herring of proof to modern philosophy).