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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