Most of the "other ways" of describing algorithms or data structures are really math in disguise, and it's easier to make the connection than it is to try to disguise it. I have only a little formal math training, but gobs of math book absorbtion. About the only things in CS that aren't really math-oriented are things such as Backus-Naur grammar descriptions for parsing, but that's only because they are application of simple declarative principles (i.e., 'formal logic') carried to a high level. Likewise, logic programming such as Prolog is very far removed from math, but only because it depends on math for its underpinnings.

As to whether a degree is a necessary thing, the answer is 'very rarely', unless your employer's customer is degree conscious, in which case it's the paper, not the understanding, that matters.