LLMs aren't totally out of scope of mathematical reasoning. LLMs roughly do two things, move data around, and recognize patterns. Reasoning leans heavily on moving data around according to context-sensitive rules. This is well within the scope of LLMs. The problem is that general problem solving requires potentially arbitrary amounts of moving data, but current LLM architectures have a fixed amount of translation/rewrite steps they can perform before they must produce output. This means most complex reasoning problems are out of bounds for LLMs so they learn to lean heavily on pattern matching. But this isn't an intrinsic limitation to LLMs as a class of computing device, just the limits of current architectures.