Is there such a thing as pure, rational knowledge? Would mathematics fall into this category?

This is a classic epistemological question asking you to engage with the debate between rationalists like Descartes and empiricists like Hume. To answer this effectively we need to make clear what the opposing sides argue, and then to make an argument in favour of one or the other.

As an example, I might argue that pure, rational knowledge is impossible. We are born tabula rasas and everything we come to know, we come to know through experience. In this way, numbers and mathematics are learnt through the repeated observations of items grouped together (for example). The rationalist would argue it is difficult to understand numbers in this way: I can count to a million (with enough time) but I've never 'experienced' a million things. The empiricist will argue back and say this is an abstraction and therefore a form of rational knowledge, but that it is based on more basic concepts like 'one' and 'plus one' which are known through experience. Therefore there is not PURE, rational knowledge.