number theory
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.
quantum computing
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.
number theory
Mathematicians Shed Light on Elliptic Curves
Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics.
Mathematics
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.
symmetry
How to Make Impossible Wallpaper
A new collection of arresting wallpaper designs seems to defy the crystallographic restriction.
traveling salesperson problem
Computer Scientists Take Road Less Traveled
An infinitesimal advance in the traveling salesman problem breathes new life into the search for improved approximate solutions.
cryptography
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.
Mathematics
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.