The 2-dimensional analog of the Kepler conjecture; the proof is elementary.

Among the best examples are the four color theorem and the Kepler conjecture.

The solution for problem 18, the Kepler conjecture, uses a computer-assisted proof.

The Kepler Conjecture is also not the first proof to rely on computers.

Current software, however cannot handle anything nearly as complex as the Kepler Conjecture.

Kepler conjecture is almost all but certainly proved algorithmically by Thomas Hales in 1998.

But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove.

What is the densest packing of spheres of equal size in space (Kepler conjecture)?

After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century.

Although it expressly includes shapes other than spheres, it is generally taken as equivalent to the Kepler conjecture.

This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one.

The Kepler conjecture.

Thomas Hales's proof of the Kepler conjecture.

The Kepler conjecture says that this is the best that can be done-no other arrangement of spheres has a higher average density.

A related problem, whose proof uses similar techniques to Hales' proof of the Kepler conjecture.

The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular.

Thomas Callister Hales (almost certainly) proves the Kepler conjecture.

Other results in geometry and topology, including the four color theorem and Kepler conjecture, have been proved only with the help of computers.

In 1998 Thomas Hales, following an approach suggested by , announced that he had a proof of the Kepler conjecture.

Mathematical problems (e.g., the Kepler conjecture)

Referees have said that they are "99% certain" of the correctness of Hales' proof, so the Kepler conjecture has very likely been proved.

In January 2003, Hales announced the start of a collaborative project to produce a complete formal proof of the Kepler conjecture.

American mathematician Thomas Callister Hales has given a computer-aided proof of the Kepler conjecture.

The Kepler conjecture is a mathematical conjecture, about Sphere packing in three-dimnsional Euclidean space.

That is why an earlier proof of the Kepler Conjecture, first offered eight years before Dr. Hales's, is rarely talked about these days.