Euclid鈥檚 Window: The story of geometry from parallel lines to hyperspace by
Leonard Mlodinow, Free Press, $26, ISBN 0684865238
GEOMETRY is of central importance in mathematics because it brings a very
powerful tool into play: the visual ability of the human mind. Unfortunately,
geometry is usually presented in terms of less friendly mental
attributes鈥攁lgebra and logic.
Euclid鈥檚 Window shows that it doesn鈥檛 have to be like that, and does
so with a deft touch. Leonard Mlodinow attempts the difficult task of presenting
geometry as a core activity in mathematics, science and human culture, and pulls
it off brilliantly.
Advertisement
His narrative takes the form of five biographical stories, each about a key
figure in the development of geometry: Euclid, Descartes, Gauss, Einstein and
Witten. Euclid of Alexandria laid the logical foundations. Ren茅 Descartes
linked geometry to algebra. Carl Friedrich Gauss discovered that there are many
geometries, of which Euclid鈥檚 is but one. Albert Einstein united space and time
in a single non-Euclidean geometry. And Edward Witten is taking important steps
towards a unified geometric setting for the whole of physics, the theory of
superstrings.
Euclid鈥檚 Window is a remarkably painless way to discover just how
central geometric thinking has been to human culture. Like its subject matter,
it is elegant, attractive and concise . . . but also very readable. Buy it.