## Latest Articles

### Together and Alone, Closing the Prime Gap

Working on the centuries-old twin primes conjecture, two solitary researchers and a massive collaboration have made enormous advances over the last six months.

### The Proof in the Quantum Pudding

How do you know if a quantum computer is doing what it claims? A new protocol offers a possible solution and a boost to quantum cryptography.

### Mathematicians Shed Light on Elliptic Curves

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.

### Unheralded Mathematician Bridges the Prime Gap

A virtually unknown researcher has made a great advance in one of mathematics’ oldest problems, the twin primes conjecture.

### How to Make Impossible Wallpaper

A new collection of arresting wallpaper designs seems to defy the crystallographic restriction.

### Computer Scientists Take Road Less Traveled

An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions.

### Privacy by the Numbers: A New Approach to Safeguarding Data

A mathematical technique called “differential privacy” gives researchers access to vast repositories of personal data while meeting a high standard for privacy protection.

### Getting Into Shapes: From Hyperbolic Geometry to Cube Complexes and Back

Thirty years after William Thurston articulated a grand mathematical vision, a proof by Ian Agol marks the end of an era in the study of three-dimensional shapes.