At 04:01 PM 9/25/2003, John Conway wrote:
>   Yes, of course.  The same argument applies to solving the game
of Chess.  If next week someone claims to have done that, I won't
believe them for the same reason, namely that the problem is so
big that their argument is more likely to be wrong than right.

I think a computer search could succeed with the 4-D kissing number problem.  I was contemplating it several years ago.  Consider for a moment the 3-D version.  Take a sphere to be the center sphere.  WOLG, place a sphere touching it.  WOLG, place the next sphere touching the center sphere and the first one, etc.   Use standard backtracking/depth first search.  I don't think there are too many possibilities to consider for the 4-D kissing number - far fewer than chess.