I'm greatly enjoying following Doron Zeilberger's glee in this paper, arxiv.org/abs/1208.2258, via @PeterKagey, as he avoids using Taylor series, then radicals, then even subtraction, to prove a result in combinatorics
In reply to @christianp
@PeterKagey he waves away operations like a sleight-of-hand magician vanishing your watch. It's a sight to behold