A quick sort sorts a list. A LLM depends on its learning data.
You train a model and then you use the model.
Algorithms can be based on training and/or use data just fine, too. https://arxiv.org/abs/1712.01208
(Now, the weights used, those we kinda really don't understand the same way we understand the processing, and the approach to looking for structures in weights sometimes looks more like archeology or anthropology than computer science.)
It sounds like you're trying to express some kind of "but LLMs are so much more" thought. Yes, very much, they are. It's because of the size of the data, there's interesting emergence there. They're still a normal algorithm. (And our brains aren't quite like that; biological things are much more random/chaotic and generally non-reproducible. And the data and algorithm aren't separate.)
For this they needed extra tools to do so.
This 'algorithm' of how the lLM does that, was unknown before their research.
Our brains are not that chaotic though. They have even more complexity to size for sure and the issue that its hard to look into a humans brain.
sufficient telemetry + sufficient compute = AI solution to any problem
From the Universal Approximation Theorem for neural nets, we know that if we have the right training method and net architecture we can get approximate any function with a NN. Of course, that doesn't imply that we actually have a sufficient training method and net architecture for the problem at hand, but we have been able to demonstrably solve at least two engineering domains: physical world navigation (Waymo) and language (GPT). It turns out a robust enough language model is sufficient for reasoning.
Given these results, I am personally stumped to come up with a problem humans can solve now that we can't solve with a computer given the correct telemetry and sufficient compute.
https://web.mit.edu/people/dpolicar/writing/prose/text/think...