Isn't it the same for anything that uses a Monte Carlo simulation to find a value? At times you'll end up on a local maxima (instead of the best/correct) answer, but it works.
We cannot solve something used a closed formula so we just do a billion (or whatever) random samplings and find what we're after.
I'm not saying it's the same for LLMs but "trying a bunch of different values and see which one works best" is something we do a lot.
I feel like most of our industry up until now has been engineered.
LLMs were discovered.
But that describes science. http://imgur.com/1h3K2TT/
To me, personally, these are 2 sides of the coin, without one having more proof than the other.
Ideally we want theoretical foundations, but sometimes random explorations are necessary to tease out enough data to construct or validate theory.
When I worked in the games industry in the 1990s, it was "common knowledge" that neural nets were a dead end at best and a con job at worst. Really a shame to lose so much time because a few senior authority figures warned everyone off. We need to make sure that doesn't happen this time.
Answering the GP's point regarding why deep learning textbooks, articles, and blog posts are full of sentences that begin with "We think..." and "We're not sure, but..." and "It appears that..."
What's yours?