Definitions, theorems and proofs
The highest form of pure thought is in mathematics.
We now come to the heart of how mathematicians organize and present their work. Look through any high-level mathematics book (or see Chapter 1) and you will find that mathematics is not presented as one continuous piece of prose like a novel. Instead the text is divided up into small nuggets of information such as a Theorem, Proposition, Lemma, Corollary, Proof, Definition and Conjecture. All of these have special meanings and we will see how to ...