Once again, you are referring to simple proofs. A spelling test is also boring.
What I am referring to is the level where math is a set of tools. Rather than doing algebra, I frequently finding myself create new algebras. Every time I create a new algebra (in order to model data, for example), I informally prove that it meets the required axioms to be the mathematical ring or group I mean it to be.
It's a whole different type of math. It's like reading shakespeare (where there are a bunch of difficult words) vs writing shakespeare (where a master of the English language invents new words to suit his purpose, while still conveying the message clearly).
Abstract Algebra is my favorite math topic. I was addicted after one semester. Proving things about groups and rings, and making up your own groups and rings makes other math feel like an engineering exercise. Making new structures and proofs redefined what I understood math to be.
What I am referring to is the level where math is a set of tools. Rather than doing algebra, I frequently finding myself create new algebras. Every time I create a new algebra (in order to model data, for example), I informally prove that it meets the required axioms to be the mathematical ring or group I mean it to be.
It's a whole different type of math. It's like reading shakespeare (where there are a bunch of difficult words) vs writing shakespeare (where a master of the English language invents new words to suit his purpose, while still conveying the message clearly).