ABSTRACT
Mathematics is an internally consistent, formal language with no necessary empirical content. Henri Poincare's work led to the development of the abstract mathematics of differential topology. Mechanics is the branch of applied mathematics concerned with the interaction of matter at the macro-level. Most scientific research up to the end of the nineteenth century was concerned with the elaboration of the principles of mechanics. Laplace in his great work on celestial mechanics argued that the solar system was indeed structurally stable. It is hardly surprising that the fundamental ideas of social mathematics, of modeling the political economy, developed in the century after Newton's Philosophiae Naturalis Principia Mathematica. Since the 1960s there has been increasing interest in exploring the possibility that complex "adaptive" systems can be found at the border between the structurally stable and chaotic systems.
