You often (but not always!) can replace a math definition with code—but either your code is sufficiently precise that it's just another way of phrasing the definition, or you're in the analogous situation to using a language defined by its implementation instead of a specification. And there's plenty of useful space for such languages—but they aren't formally specified languages. Math that isn't formally specified isn't math, in any sense that a mathematician would recognize—which is not to say that it can't be useful.