> while my calculator can perfectly add any numbers up to its memory limit, it has no understanding of addition.
"my calculator can perfectly add any numbers up to its memory limit" This kind of anthropomorphic language is misleading in these conversations. Your calculator isn't an agent so it should not be expected to be capable of any cognition.
> If you built an LLM exclusively on the writings and letters of John Steinbeck, you could NOT tell the LLM to solve an integral for you amd expect it to be right.
Isn't this obvious? There is not enough latent knowledge of math there to enable current LLMs to approximate anything resembling an integral.