In 8 Dimensions Exactly 240 Spheres Touch

Take one ball and surround it with identical balls, all touching it, none overlapping. On a line you fit 2. In the plane you fit 6, and there is no room to spare. In three dimensions the answer is 12 — Newton said 12, Gregory thought 13 might fit, and nobody settled it until 1953. CHAPTERS 0:00 How Many Can Touch One 1:11 Two Different Questions 2:24 Kepler Took 387 Years 3:34 It Gets Worse Before It Gets Better 4:47 E8 6:05 The Leech Lattice 7:32 The Bound Nobody Could Reach 8:45 Viazovska 10:02 Why Those Two 11:14 Everything Else Is Open Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a...