I'm reading through Morris Kline's 1967 book Mathematics for the Nonmathemetician. I got a math minor in college, eking through two semesters of calculus, but would like a refresher both for personal improvement and for the eventual education of the children. This won't be in-depth explanations, but notes on whatever I find interesting.
Chapter 1 - Why Study Math?
Mathematics is difficult to define. Kline's attempt is: mathematics is what mathemetics does. It concerns the work of reason, primarily to study nature. We study nature to understand nature, fulfilling intellectual curiousity (and I would say, as part of the dominion mandate and the journey to become as human as possible).
It's practical purpose is to aid science. It also aids art, particularly music.
It helps us acquire truth and has affected our philosophy and religion (although Kline admits to not having a final answer on what truth is, or how it is acquired.)