The hexagonal honeycomb conjecture
The classical hexagonal honeycomb conjecture asserts that
the most efficient partition of the plane into equal areas is
the regular hexagonal tiling. In June 1999, I found a proof of
the conjecture.
To obtain the paper:
Here is an expository article, Cannonballs and Honeycombs, that
describes the solution to the Kepler Conjecture and the Honeycomb
Conjecture. (The graphics have not been inserted yet, but they are
not essential.)