From a 1D line to the mind-bending worlds of 8D and 24D, this episode unpacks the kissing number problem—the maximum number of identical spheres that can touch a central sphere without overlap. We'll trace the Newton-Gregory debate in 3D, celebrate Musin's 2003 proof, and reveal the magic of the E8 and Leech lattices that pin down exact numbers in certain dimensions. Along the way we glimpse why computing these arrangements remains a frontier of mathematics and computer science.

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