1) 2) 3) It's necessary to know some words to write poetry.
But when you write poetry, you are speaking about soul.


1) .. 3) Math as a tool for your work give you shortcut.
To be a good programmer need programming xp-rience and insight.

1) In mathematic field yes, in real word you just need to be able to describe formally a problem. Solutions can breaks some rules, math cannot (do you use strict:))

2) They will get a better salary for sure!
All algorithm doesn's need an hardware knowledge

3) You should get a look at Perl :)