It’s more like educated guessing, which is a lot faster than brute forcing. They can use code to check the answers so there is ground truth to verify against. A few days of compute time for an answer to a previously unsolved math problem sounds a lot better than brute forcing.
Generate enough data for good guesses and bad guesses and you can train the thing to make better guesses.
“Do your own research” is a phrase with a lot of baggage. It means more than doing your own research.
It’s a phrase that has been used online in debates over every kind of conspiracy theory, religious idea, or political stance and carries with it the unsaid presumption that alternative sources are the key to learning the “actual truth.” It’s a loaded phrase that acts as a calling card for people who are overly confident that they have the right answer but can’t articulate how they arrived at it.
I roll my eyes whenever I read or hear someone say “do your own research” because I know the debate ends there and there’s no convincing them otherwise.