But since Turing's time we've known that intelligence is just computation--it's not until recently that we've been able to come up with the specific algorithm.
Think back to Kasparov playing Deep Blue. Back then, some people (including Kasparov) believed that a computer would never beat a human. They felt that human creativity and ability to see the whole board would always beat brute-force computation.
I watched the pivotal game 5 live. There was a point where Deep Blue made a pawn move away from the main action. The commentators at the time, chess master all, almost cheered--it looked like the machine had blundered. "It's playing like a computer" they said. But one look at Kasparov told you they were wrong. Kasparov was worried. The main action resolved, but in the end, that one pawn move, 20 moves prior, left Deep Blue in a better position.
What modern LLMs do is apply brute-force computation to any domain expressible in language--not just a restricted chess domain. That's the algorithm.