A slight oversimplification, as LLMs are also capable of generating the most statistically plausible textual sequence, which can be a sequence not found in the dataset but rather a synthesized combination of the likely sequences of multiple preceding sets of tokens, but yes, that is in fact what it is doing. Computer software does what it is programmed to do, and LLMs are not programmed to do logical inference in any capacity but rather operate entirely on probabilities learned from a mind-bogglingly large corpus of text (influenced by things like RLHF, which is still just massaging probabilities).

The claims about solving Erdos problems have been wildly overstated, and notably pushed by people who have a very large financial stake in hyping up LLMs. Nonetheless, I did not say that LLMs are useless. If they are trained on sufficient data, it should not be surprising that correct answers are probabilistically likely to occur. Like any computer software, that makes them a useful tool. It does not make them in any way intelligent, any more than a calculator would be considered intelligent despite being completely superior to human intelligence in accomplishing their given task.