A Possible Mathematical Structure for Physics

The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real, $\mathbb{R}$, the complex, $\mathbb{C}$, and the quaternion, $\mathbb{H}$ - known to meet the requirements of a mathematical description of our universe. The known forces and particle structure, in terms of families and color, can be associated with natural relationships within that structure. A "toy" scientific theory - based on the proposed mathematical structure - is presented to illustrate its applicability. It is shown how parity and time reversal invariance are broken. Two relevant predictions come from the formalism. First, there are no gravity waves and second, matter comes in three varieties, one of which is "dark" in the sense that it is oblivious to electromagnetic interactions.