Slicing All Edges of an N-Cube Requires N^(2/3) Hyperplanes

Watch a 57-minute mathematics lecture exploring the fascinating problem of determining the minimum number of hyperplanes needed to dissect all edges of an n-cube graph in n-dimensional space. Delve into a geometric puzzle that has remained unsolved since the 1970s, examining vertices with Hamming distance 1 and the connections between them in {0,1}^n space. Learn why n hyperplanes are sufficient for edge dissection while sqrt(n) proves inadequate, and discover the mathematical reasoning that leads to the n^(2/3) hyperplane requirement. Presented by Ohad Klein at the Hausdorff Center for Mathematics, this advanced geometric topology lecture provides deep insights into cube slicing problems and their mathematical implications.