Mathematics

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

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

New data collected by mathematicians and oceanographers in the frigid waters of the Southern Ocean could dramatically improve climate models.

In an increasingly interconnected world, scientists are seeking safeguards against catastrophic cascades of failure like stock market crashes and widespread blackouts.

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.

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

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.