Author(s): Shigeko TakahashiWith the camera-type eyes which have a specialized function for the image-forming vision, the primary visual cortex (V1) is common to all mammalian species, and is considered to be established at early stage in mammalian evolution, being inherited in all lineages. A defining characteristic of the mammalian V1 is the presence of orientation-selective neurons (or simple cells), which are activated in response to line-, or edge- stimuli in some orientations better than others. It is not yet known as for what were the driving forces that made the robust emergence of such a common design for V1 neurons in mammalian evolution. In this study, I address this problem by employing mathematical approach to arithmetizing various kind of geometries. The formalism which I employ here can not only account for an essential role of the receptive field organization of orientation-selective V1 neurons to the processing of images, but also be used to focus in a concise way to develop mathematical logic as a model of how visual neurons work.