>if you are honest and pragmatic and someone asked you how you added two numbers, you would only say you did long addition if that's what you actually did. If you had no idea what you actually did, you would probably say something like "the answer came to me naturally".

To me that misses the argument of the above comment. The key insight is that neither humans nor LLMs can express what actually happens inside their neural networks, but both have been taught to express e.g. addition using mathematical methods that can easily be verified. But it still doesn't guarantee for either of them not to make any mistakes, it only makes it reasonably possible for others to catch on to those mistakes. Always remember: All (mental) models are wrong. Some models are useful.