If a script were applied that corrected "bad math" and now the LLM could solve complex math problems that you can't one-shot throw at a calculator, what would you call it?
But this math analogy is not quite appropriate: there's abstract math and arithmetic. A good math practitioner (LLM or human) can be bad at arithmetic, yet good at abstract reasoning. The later doesn't (necessarily) requires the former.
In chess, I don't think that you can build a good strategy if it relies on illegal moves, because tactics and strategies are tied.
Applying a corrective script to weed out bad answers is also not "one-shot" solving anything, so I would call your example an elaborate guessing machine. That doesn't mean it's not useful, but that's not how a human being does maths, when they understand what they're doing - in fact you can readily program a computer to solve general maths problems correctly the first time. This is also exactly the problem with saying that LLMs can write software - a series of elaborate guesses is undeniably useful and impressive, but without a corrective guiding hand, ultimately useless, and not demonastrating generalised understanding of the problem space. The dream of AI is surely that the corrective hand is unnecessary?
I was once asked by one of the Clueless Admin types if we couldn't just "fix" various sites such that people couldn't input anything wrong. Same principle.