I think it is worth summarizing the assumptions that we make about solving chess:
1) We demand a strong solution
2) In order to have a strong solution you need a memory capable of storing the outcome of all legal positions ( save simple symmetries )
3) The number of legal positions in chess is not significantly lower than the proven upper bound of 10^46
4) Chess is computationally irreducible ( that is only exhaustive brute force tree search works )
Given the assumptions above there is nothing that makes chess unsolvable, but the solution seems extremely hard, and will take time.
If you hope for a quick solution you have to drop one or more of the above assumptions and give good reasons for doing so.
"Never" in our lifetimes, but it's still a draw with best play, because white cannot force a win.
Topology ain't got nothing to do with it. Sorry.
You might as well watch the movie, The Day the Earth Stood Still (1951), and then continue to dream-on.
And Please, be relevant, helpful & nice!