Intelligence and consciousness are still topics in scientific research, involving a lot of unsolved questions. Roger Penrose tries to explain some aspects with one of Gödel's incompleteness theorems and noncomputability, where the latter might be connected to the collapse of the wave function in quantum mechanics. With this connection consciousness and human identity might be an epiphenomenon of quantum physics.
WP: Kurt Gödel WP: Gödel's incompleteness theorems WP: Computability theory WP: Wave function collapse