This article employs an interdisciplinary approach to explore some psychological dimensions of mathematical creativity and the dogmatism that can emerge when mathematical applications are confined within a single worldview. More specifically, it explores some ways in which mathematics has been confined and distorted in service of dogmatic conceptions of important phenomena, and for various purposes, some unwittingly damaging and others wittingly nefarious. Some of the topics dealt with include the dogmatic use of distorted mathematical modeling in economics, the sterile certainty that arises from excessive entrapment within the mechanistic worldview in various disciplines, and the dogmatism of artificial precision in educational reform initiatives. Methods for breaking free of dogmatism and for injecting ethics into mathematical applications also are explored.