The subcritical brain : a synergy of segregated neural circuits in memory cognition and sensorimotor control Have over a hundred years of brain research revealed all its secrets This book is motivated by the realization that the mathematical theory of dynamical systems underlies cortical behavior. This realization is further enhanced by the synergy of seemingly different mathematical notions: global attractors which define non invertible neural firing rate dynamics random graphs which define connectivity of neural circuit and prime numbers which define the dimension and category of cortical operation. Quantum computation is shown to ratify the main conclusion of the book: loosely connected small neural circuits facilitate higher information storage and processing capacities than highly connected large circuits. While these notions have not been commonly involved in the evolution of neuroscience they are shown in this book to play a fundamental role in the description of cortical behavior. Furthermore neurophysiological experiments as well as observations of natural behavior and evidence found in medical testing of neurologically impaired patients are shown to support and to be supported by the mathematical findings