Artificial intelligence is breathing down our necks: Software built by Google startled the field last week by easily defeating the world’s best player of the Asian board game Go in a five-game match. Go resembles chess in the deep, complex problems it poses but is even harder to play and has resisted AI researchers longer. It requires mastery of strategy and tactics while you conceal your own plans and try to read your opponent’s.

Mastering Go fits well into the ambitious goals of AI research. It shows us how much has been...