While mathematical economic theory is replete with structural relationships, it has been suggested that economists have been far to content with the structure created in their conceptual theoretical worlds, and have done too little to conceptualise or study the structure inherent in actual economic systems. I advance the state of the argument by proposing a typology of theory types - correspondence, instrumental, speculative, and literary - with differing attempts and approaches to building some kind of 'correspondence' between the ontological elements (...) and relationships in the real world and the ontological elements and relationships in the theoretical world. The central argument advanced in the present paper is that the use of mathematics in economics is of a fundamentally different nature than the use of mathematics in, for example, physics. In physics an attempt is made to capture the central and important features of the real world in mathematical equations, and a deeper understanding of the dynamics and relationships in the real world is gained as a consequence. In economics, by contrast, the use of mathematics does little to identify, abstract and capture the structure existing in real world social and economic systems. The use of mathematics may make economic theories very precise, may exclude individuals without extensive training to access economic theories, and may perform a rhetorical service in presenting economic theory as mathematical and, by analogy with physics, scientific. In many cases, however, the net effect of using mathematics in economic theory is the precise opposite of the effect of using mathematics in physics: in physics, mathematics brings us a greater focus on and awareness of structures and relationships in our physical reality, while in economics mathematics takes us away from a focus on and concern with the ontologies and structures in real world economic systems and focuses our attention on abstract, invented theoretical worlds often with unclear relationships to actual economic systems. (shrink)