Douglas Hofstadter, the Pulitzer Prize–winning author of Gödel, Escher, Bach, thinks we've lost sight of what artificial intelligence really means. His stubborn quest to replicate the human mind.

For over two millennia, mathematicians agreed on one thing: you can’t use trigonometry to prove Pythagoras’ Theorem—because trigonometry is built on it. That logic, drilled into students and scholars ...