This article is from the Go FAQ, by Morten PAHLE email@example.com with numerous contributions by others.
Yes. Considering that Go is a 'complete knowledge' game, there must be
a way to play which is optimal for both players, and which leads to an
Despite this result of general game theory, human players are very far
from perfect play. It is extremely likely that the best moves (even in
the early opening) have yet to be played.
The truth is that Go is so complex that it is impossible to say, for
almost any given situation, with 100% certainty, which is the best
move. Doing this for a whole game is even harder.
The above is true even for small board sizes.
Several threads on rec.games.go have discussed this for various board
sizes and various rule sets. Even for 2x2 boards, this is not a
trivial task, and the result varies widely with the basic ruleset
For larger boards, this becomes even harder.
Even the almost obvious postulate: "Black plays first so he should
also win" has never been proven nor disproven.
It also follows that there is no 'perfect' value for komi at various
board sizes, indeed, it is open for argument whether or not komi
should be adjusted (and how) according to board size.