Hancock, N.H. – Anyone faced with the task of building a freestanding pile of spheres quickly discovers an obvious solution: Start by laying out the densest possible two-dimensional packing and then ...

Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...

经过短短几个月的努力，球体堆积领域的一个新人解决了该领域最大的未解问题之一。 在数学中，对最优模式的探索永无止境。球体堆积问题（sphere-packing problem）——即如何尽可能高效地将球塞进一个（高维）盒子——也不例外。几个世纪以来，它一直吸引着 ...

HANCOCK, N.H. — Anyone faced with the task of building a freestanding pile of spheres quickly discovers an obvious solution: Start by laying out the densest possible two-dimensional packing and then ...

A group of mathematicians has announced a milestone in the effort to thoroughly verify the solution of the sphere-packing problem — for which the Ukrainian mathematician Maryna Viazovska won the ...

In 1611 German mathematician Johannes Kepler made a conjecture about the densest way to stack oranges or other spheres with a minimum of space between them. It seemed nothing could beat the standard ...