The Sphere-Packing Problem in High Dimensions #mathematics

Video Description

The sphere-packing problem is simple to state: How do you arrange identical spheres to fill as much volume as possible without overlapping? In three dimensions, you can arrange spheres in a pyramid-shaped pile, the way oranges get stacked in a grocery store. But what about in higher dimensions? In April, Quanta reported on the first significant advance on this version of the sphere-packing problem in 75 years. The result improved on the efficiency of previous packings, while making use of a novel approach: Rather than packing spheres in a nice, organized way, the mathematicians used graph theory to pack spheres in a very disorderly fashion. Mathematicians don't just try to find optimal arrangements in specific dimensions. They also want to find a general solution — a formula that gives a way to densely pack spheres in arbitrarily high dimensions, even if the packing isn’t completely optimal. Watch the full video: https://youtu.be/lwVSeXswWZY?feature=shared Read the article: https://www.quantamagazine.org/to-pack-spheres-tightly-mathematicians-throw-them-at-random-20240430/ Paper: " A new lower bound for sphere packing" https://arxiv.org/abs/2312.10026 --------- - VISIT our website: https://www.quantamagazine.org - LIKE us on Facebook: / quantanews - FOLLOW us Twitter: / quantamagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org