## Latest Articles

### New Proof Shows That ‘Expander’ Graphs Synchronize

The proof establishes new conditions that cause connected oscillators to sway in sync.

### 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?

### 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.

### 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.

### Quantum Field Theory Pries Open Mathematical Puzzle

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

### Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

### Probability and Number Theory Collide — in a Moment

Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories.

### From Systems in Motion, Infinite Patterns Appear

Mathematicians are finding inevitable structures in sufficiently large sets of integers.