The idea of chaos figures prominently in mathematics today. It
arose in the work of one of the greatest mathematicians of the late 19th
century, Henri Poincaré, on a problem in celestial mechanics: the
three body problem. This ancient problem—to describe the paths of
three bodies in mutual gravitational interaction—is one of those
which is simple to pose but impossible to solve precisely.
Poincaré's famous memoir on the three body problem arose from
his entry in the competition celebrating the 60th birthday of King
Oscar of Sweden and Norway. His essay won the prize and was set up in
print as a paper in Acta Mathematica when it was found to
contain a deep and critical error. In correcting this error
Poincaré discovered mathematical chaos, as is now clear from
Barrow-Green's pioneering study of a copy of the original memoir
annotated by Poincaré himself, recently discovered in the
Institut Mittag-Leffler in Stockholm.
Poincaré and the Three Body Problem opens with
a discussion of the development of the three body problem itself
and Poincaré's related earlier work. The book also
contains intriguing insights into the contemporary European
mathematical community revealed by the workings of the competition.
After an account of the discovery of the error and a detailed
comparative study of both the original memoir and its rewritten version,
the book concludes with an account of the final memoir's reception,
influence and impact, and an examination of Poincaré's subsequent
highly influential work in celestial mechanics.
Readership
Graduate students, mathematicians, astronomers,
and physicists interested in an historical perspective
of mathematics.
