I want to mention something which is probably at the core of why I am still slightly apprehensive about pure mathematics. When I was at school and studying for Maths 'O' level back in the late 70's, we were taught a new fangled type of maths called SMP mathematics (SMP stands for "School Mathematics Project"). I found it really difficult to understand as it was a new way of teaching mathematics that contained a high proportion of pure maths ideas.
The trouble was that these ideas were often taught without explaining why they were needed. I can still recall learning about matrices, determinants and transformations of the unit square. It all sounded like gobbledygook to me as I couldn't relate it to anything else we were learning. So, for example, we were taught how to work out the determinant of a 2x2 matrix, but there was no explanation of why we were doing it. It also didn't help that we had a maths teacher who insisted that we just listen to his explanations without being able to take notes and then work at numerous examples. I just couldn't work like this and I can remember once that I received a very poor 5/95 for a maths test!
Needless to say I didn't do well in my 'O' level and it wasn't a subject that I wanted to take for 'A' level. The trouble was that I was very interested in physics and astronomy and in the end I wanted to do an astrophysics degree. So, I ended up cramming a maths A level into a year at a different college. That's when my maths finally blossomed as I was taught the more basic 'relevant' maths which I was more comfortable with.
So since that time, I have always been somewhat fearful of pure mathematics in case I find myself floundering again.
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