Summary: The Pursuit of Perfect Packing. By Tomaso Aste and De-
nis Weaire. Institute of Physics Publishing, Bristol, U.K.,
2000, xi + 136 pp., ISBN 0-7503-0648-3, $32.30.
Kepler's Conjecture. By George G. Szpiro. Wiley, Hobo-
ken, NJ, 2003, viii + 296 pp., ISBN 0-471-08601-0, $24.95.
Reviewed by Charles Radin
In 1990, from news flashes on television and in newspapers, the whole
world heard of W.-Y. Hsiang's announcement of a proof of the "sphere
packing conjecture" on the most efficient way to pack equal spheres in
space. This was followed by the equally well-publicized announcement
of another proof by T. Hales in 1998. Definitive versions of their argu-
ments have yet to be published, so I will not make any pronouncements
on the status of their work--tempting as that might be!
Mathematical results do not often receive such publicity, so why
all the attention to this problem? Two reasons come quickly to mind.
The first is its long history: the conjecture can be plausibly traced back
four hundred years to Kepler and is sometimes designated by his name.
The other is that the conjecture can be stated in plain English without
the need of esoteric terminology. Those two features are attractive to
journalists but do not explain the interest of the mathematical research