Convex Geometry Cracks Decades-Old Sphere Packing Problem

A decades-old problem in mathematics, the efficient packing of spheres in high-dimensional space, has been significantly advanced. Professor Boaz Klartag, using a novel approach from convex geometry, cleverly improved an existing method, achieving a substantial increase in packing efficiency. By using a random process to adjust an ellipsoid, he found a more efficient way to pack spheres than any previous method, improving efficiency by hundreds or even millions of times in high dimensions. This breakthrough not only sets a new record for sphere packing but also reignites the debate on the optimal sphere packing in high-dimensional space, offering new insights for cryptography and communications.