Well, while training AI we make sure that we include enough training for them to pass some evaluation, but then test them on things that were not in the training data to make sure that they are not "over fitted".
It's kind of like asking what even is IQ if you can learn how to solve Mensa puzzles and improve your score. Does it mean you're more intelligent?
One guess for GPT4 is that it's an amalgamation of models. So you would have various models trained more specifically like the ones you mentioned, and you ask them all to start answering the query, then you choose which one produces better results, and then you present that to the user.
Alternatively you can have a decider model that knows what kind of queries goes to what specialised one, then have that as a "hidden layer", whether it be in the application level or "neuron layers".
Under a narrow range of tests specialization is pretty much guaranteed to win. Specialization in all cases I know of comes at a cost to general capability. It's like one of those qips "Pick any two: fast, cheap, good", the more you pull at one category, the costs rase in the other categories.