It's a good point. 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

It's a good point. 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.