In May of 1694, Isaac Newton and David Gregory stumbled upon a math puzzle while contemplating stars’ orbits around a central sun. The problem, known as the “kissing problem,” involves arranging spheres around a central one without overlapping. While the maximum “kissing number” in three dimensions is 12, it varies in other dimensions, and recent groundbreaking work by Anqi Li at MIT has challenged conventional methods by deliberately introducing disorder into sphere packings. This approach, deviating from symmetry, has led to exciting advances in the kissing problem and sheds light on the mysteries still surrounding this mathematical puzzle.
https://www.quantamagazine.org/mathematicians-discover-new-way-for-spheres-to-kiss-20250115/