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
.
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