It is just nuts that this kind of reasoning works out reliably.
For chess positions where there is no tactic that gives a clear advantage, the best move is determined by subtle positional/strategic considerations. It's interesting that often, top players will all agree what the best move is, but be incapable of explaining why except in very vague terms. It just "feels right".
I haven't read about computer chess in a while so I'm not sure if this is still the case, but at least for several years after it became impossible for a human to beat a computer, a human+computer team was still much stronger than a computer alone, because of this intuitive strategic/positional ability that computers lack.
I guess to explain my comment a bit further: I conjecture (as a pure layman) that a similar process is going on when a chess grandmaster says "I played Nf7 because it looked natural" as when a mathematician says "I expect this statement to be true for aesthetic/intuitive/moral reasons".
I think in this case the mathematician's unconscious mind has correctly identified some pattern that his or her conscious mind is unable to access.
Just like I can't really explain why I know my dad's face is his, and not that of some other man of similar race, age, and build.
The algorithm itself doesn't seem particularly aesthetic.