Trained as a mathematician, in the area of nonlinear dynamical systems in particular, I have been fascinated by the most intriguing dynamical system of all, the brain. In this talk, I will report on some ongoing work in which my co-authors and I seek to model the monkey visual cortex, which is very similar to our own, as a large and complex dynamical system. I will focus on the primary visual cortex (V1), where the first stage of visual information processing begins. I will discuss the anatomical facts gleaned from biology, how they were used to build a mathematical model, the experimental data used for validation, the analysis of dynamical mechanisms, and finally, how this modeling work has shed light on some basic issues in visual neuroscience.