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# Ramsey theory

## Latest Articles

### The Year in Math

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

### The Lawlessness of Large Numbers

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

### Mathematicians Discover Novel Way to Predict Structure in Graphs

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

### A Very Big Small Leap Forward in Graph Theory

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

### Why Mathematicians Re-Prove What They Already Know

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

### Coloring by Numbers Reveals Arithmetic Patterns in Fractions

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.

### Math’s ‘Oldest Problem Ever’ Gets a New Answer

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

### Mathematician Hurls Structure and Disorder Into Century-Old Problem

A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

### New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.