The term Superconmath means Superconceptual Mathematics. It is a meta-mathematical system that defines the structure of Superultramodern Mathematical Science. Superconmath proposes that the conventional (i.e. pre-superultramodern or modern/ultramodern) mathematical science is not as conceptual as it should be. In other words, it has conceptual deficiencies, in nature as well as in approach. Superconmath has five main components: 1.Superconceptual Definition of Mathematics 2.Philosophy as Mathematics 3.Superconceptual Foundations of Pure mathematics 4.Superconceptual Reconstruction of Pure Mathematics 5.Superconceptual mathematical Resolution of Modern/Ultramodern Mathematical Problems This work states each of the five components, in brief.