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# Erdős conjecture

## 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.

### 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.

### Mathematicians Solve Long-Standing Coloring Problem

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

### 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.

### First-Year Graduate Student Finds Paradoxical Set

No two pairs have the same sum; add three numbers together, and you can get any whole number.

### 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.

### Surprise Computer Science Proof Stuns Mathematicians

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

### Mathematicians Settle Erdős Coloring Conjecture

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.