Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumentation and development of computer systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This veritable revolution has already resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical techniques developed for the study of complex nonlinear systems and chaos are already being used to explore the complex nonlinear dynamics of human brain physiology.