E8 Lattice: Optimal Packing in Dimension 8
E8Lattice Dimension8 LatticeTheory ExceptionalStructures
In 2016, Maryna Viazovska proved the E8 lattice provides optimal sphere packing in eight dimensions—a breakthrough solving a problem where most dimensions remain unsolved.
Sphere Packing: Kepler to Higher Dimensions
SpherePacking KeplerConjecture Optimization DiscreteGeometry
Sphere packing asks: what arrangement fits the most spheres in limited space? Grocery stores stack oranges in pyramids—this intuitive pattern is mathematically optimal in three dimensions.
Viazovska's Proof: Fourier Analysis for Sphere Packing
FourierAnalysis FieldsMedal ElegantProofs ModularForms
Maryna Viazovska received the 2022 Fields Medal for her 2016 proof of optimal eight-dimensional sphere packing using Fourier analysis and modular forms.