[lanstin]

As some one who loves SICP and first principles, I had a new math curriculum and loved it. Being able to derive the laws of arithmetic is usually a lot more useful than just knowing some particular instance of calculation.

To be sure, I also did math contests in high school to bump up my speed at math, and in software will do timed speed tests (self devised on certain types of small tasks) also to bump up my speed in a particular language.

[hnfong]

You do know how the "first principles" came into place, right?

They had arithmetic first. People counted chickens, sheep, coins first. Then, mathematicians invented more abstract rules that incidentally were able to derive arithmetic, and called them "first" principles. Chronologically they came last.

[lanstin]

I love axiomatic set theory and the history of maths and science. I love knowing how technology developed over the last few thousand years, Egyptian land measuring and trade accounting etc., and as much quantum field theory as I can understand (not that much, it's very hard). I like knowing about DNA and the history of animal husbandry. Deriving calculus and complex analysis from ZFC gives us tremendous intellectual power as far as the essentially and inherently true. Understanding how our culture has been lifting the vails of ignorance thru science and experiments and cultural evolution and so on is also important.