August 22, 2006
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Beginnings
“Nothing ever begins.
There is no first moment; no single word or place from which this or any other story springs.
The
threads can always be traced back to some earlier tale, and to the
tales that preceded that; though as the narrator’s voice recedes the
connections will seem to grow more tenuous, for each age will want the
tale told as if it were of its own making.”– Clive Barker, Weaveworld
“No mathematical subject lies closer to intuition than the geometry of two and three dimensions.”
– Robert E. Greene, beginning an April 1998 review of Three-Dimensional Geometry and Topology, by William P. Thurston
Thurston’s book provides some background for today’s opening lecture by Richard Hamilton, “The Poincare Conjecture,” at the beginning of the International Congress of Mathematicians in Madrid.
Hamilton is likely to discuss the Poincare conjecture in the wider context of Perelman‘s recent work on Thurston’s geometrization conjecture.
In “The Eight Model Geometries,” section 3.8 of his book, Thurston provides yet another beginning–
“What is a geometry?”
