The mainstream economics in both its micro and macro search for relevance in respect to people, organizations', and countries' behavior lays its analytical foundations on a rigorous set of methodological requirements. It is the purpose of this contribution to enlist the main lines of attack against that widespread belief, as well as to provide a substantial discussion as to the extent of the use of mathematical formalism distorts the significance of economic facts. To that end, this material has made recourse to the existing literature and has organized it around two dominant points of argumentation. A first cluster of arguments has been gathered along the history of economic thought with regards to the quantitative adoption of formalism from the point the view of its economic relevance. A second view tackles the issue of alternative perspectives in order to find a way out toward economic relevance. The reader is advised not to take this material as an exercise in refuting mathematical formalism in economics. Instead, its added value should reside in identifying the limits of formalism under those circumstances when the significance of economic analysis either becomes of no practical importance or assumes doubtful theoretical constructions.