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# Combinatorics

## Latest Articles

### Grad Students Find Inevitable Patterns in Big Sets of Numbers

A new proof marks the first progress in decades on a problem about how order emerges from disorder.

### Merging Fields, Mathematicians Go the Distance on Old Problem

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

### Math That Connects Where We’re Going to Where We’ve Been

Recursion builds bridges between ideas from across different math classes and illustrates the power of creative mathematical thinking.

### The Surprisingly Simple Math Behind Puzzling Matchups

If Anna beats Benji in a game and Benji beats Carl, will Anna beat Carl?

### The Year in Math

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

### A Triplet Tree Forms One of the Most Beautiful Structures in Math

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### The Astonishing Behavior of Recursive Sequences

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

### The Biggest Smallest Triangle Just Got Smaller

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.