The 400-year-old Kepler conjecture asserts that no packing of
congruent balls in three dimensions can have a density exceeding
the familiar pyramid-shaped cannonball arrangement. In this book, a
new proof of the conjecture is presented that makes it accessible
for the first time to a broad mathematical audience. The book also
presents solutions to other previously unresolved conjectures in
discrete geometry, including the strong dodecahedral conjecture on
the smallest surface area of a Voronoi cell in a sphere packing.
This book is also currently being used as a blueprint for a
large-scale formal proof project, which aims to check every logical
inference of the proof of the Kepler conjecture by computer. This
is an indispensable resource for those who want to be brought up to
date with research on the Kepler conjecture.
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