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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.

Yitang Zhang

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.

climate science

The Ocean’s Dynamic Role in Climate Change

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


Treading Softly in a Connected World

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


How to Make Impossible Wallpaper

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


In Computers We Trust?

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


In Mysterious Pattern, Math and Nature Converge

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


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.