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combinatorics
geometry
A New Path to Equal-Angle Lines
Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.
combinatorics
Simple Set Game Proof Stuns Mathematicians
A new series of papers has settled a long-standing question related to the popular game in which players seek patterned sets of three cards.
geometry
Sphere Packing Solved in Higher Dimensions
The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.
Mathematics
Theorists Draw Closer to Perfect Coloring
A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof.
Q&A
The Connoisseur of Number Sequences
For more than 50 years, the mathematician Neil Sloane has curated the authoritative collection of interesting and important integer sequences.
Multimedia
The Nine Schoolgirls Challenge
Solve this variation of Thomas Kirkman’s famous 1850 puzzle by arranging girls in walking groups. And think fast — the clock is ticking.
Mathematics
A Design Dilemma Solved, Minus Designs
A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.
Mathematics
For Persi Diaconis’ Next Magic Trick …
A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”