Henri Poincare was a French mathematician, living at the turn of the century, who made many fundamental contributions to mathematics and was an influential philosopher of science. In the natural sciences he is best appreciated for his highly original work on celestial mechanics. Through his innovations he founded qualitiative dynamics---the mathematical theory of dynamical systems.
He created topology, the study of shapes and their continuity, and used this new mathematical tool to attempt to answer a very longstanding question, Is the solar system stable? At the end of the 19th century this question was re-posed by King Oscar II of Sweden with a cash prize promised to whomever answered it definitively.
In attacking the problem Poincare limited his sights to the restricted problem of just three bodies moving under their mutual gravitational attraction. He won the prize with his publication of "On The Problem of Three Bodies and the Equations of Equilibrium". But through this investigation Poincare came to understand that infinitely complicated behaviors could arise in simple nonlinear systems. Without the benefit of computers, only through his mathematical insight and his calculational abilities, he was able to describe many of the basic properties of deterministic chaos.