Both are incredible! 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 s

Both are incredible! 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.