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.

# Articles tagged 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.

### Sphere Packing Solved in Higher Dimensions

The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.

### 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.

### 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.

### 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.

### A Design Dilemma Solved, Minus Designs

A 150-year-old conundrum about how to group people has been solved, but many puzzles remain.

### For Persi Diaconis’ Next Magic Trick …

A mathematician who has analyzed card shuffling for decades is tackling one final nemesis: “smooshing.”