## Latest Articles

### Hypergraphs Reveal Solution to 50-Year-Old Problem

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

### Mathematical Connect-the-Dots Reveals How Structure Emerges

A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

### Unimaginable Surfaces Discovered After Decades-Long Search

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

### How Complex Is a Knot? New Proof Reveals Ranking System That Works.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

### Mathematicians Coax Fluid Equations Into Nonphysical Solutions

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

### New Proof Illuminates the Hidden Structure of Common Equations

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

### In New Math Proofs, Artificial Intelligence Plays to Win

A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.

### Mathematicians Prove 30-Year-Old André-Oort Conjecture

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.

### Mathematician Answers Chess Problem About Attacking Queens

The *n*-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.