If you think there is nothing problematic or mysterious about a symbol system solving problems, then you are a child of today, whose views have been formed since mid-century. Plato (and by his account, Socrates) found difficulty understanding even how problems could be entertained, much less how they could be solved. Let me remind you of how he posed the conundrum in the Meno:
And how will you inquire, Socrates, into that which you know not? What will you put forth as the subject of inquiry? And if you find what you want, how will you ever know that this is what you did not know?