Kant: mathematics

According to Kant, the truths of arithmetic and geometry are synthetic judgments because they contribute significantly to our knowledge of the world. But these judgments are also a priori because they universally apply to all objects of our experience, without having been taken from the experience itself. The question then becomes, how do we come to have such knowledge? One might think that we indeed come to know these things through experience, rather than a priori. After all, you need to be familiar with numbers to even understand what 2 + 5 = 7 means. Kant argues that we know these things a priori because of "pure forms of sensible intuition," and not experience. He believes that things in arithmetic are directly associated with things in time, and things in geometry are directly associated with things in space. Space and time are absolute and derived from our minds. So, our concepts of space and time allow for us to understand mathematical concepts without being exposed to those concepts.