Mathematical Aesthetic Principles/nonintegrable Systems

Mathematical aesthetics is not usually discussed as a separate discipline, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as aesthetic and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, ie. the results of integration depend on the integration path. The topic of nonintegrable systems is discussed.