Three “extremely large telescopes” poised to begin observations within a decade could help answer some of the universe’s oldest and best-kept secrets.

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

As the role of computers in pure mathematics grows, researchers debate their reliability.

All complex correlated systems, from Arctic melt ponds to the Internet, appear to be governed by the same math as a random matrix.

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

Game theorists have developed a new model of communication among animals. It suggests evolution will produce a situation in which members of a species are honest most of the time, but not always.

If a new hypothesis about black hole firewalls proves correct, at least one of three cherished notions in theoretical physics must be wrong.

Computer scientists are finding that “thinking quantumly” can lead to new insights into long-standing problems in classical computer science, mathematics and cryptography, regardless of whether quantum computers ever materialize.

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