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

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.

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.

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

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

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.

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