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Trefoil vortex knot.
fluid dynamics

Could Knots Unravel Mysteries of Fluid Flow?

By investigating the central role played by knots in fluids and fields, physicists hope to unravel long-standing mysteries of turbulence.

Image of spiral staircase.

To Settle Infinity Dispute, a New Law of Logic

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth.

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.

Data Driven: The New Big Science

The Mathematical Shape of Things to Come

Scientific data sets are becoming more dynamic, requiring new mathematical techniques on par with the invention of calculus.

Illustration of an amplituhedron.
theoretical physics

A Jewel at the Heart of Quantum Physics

Physicists have discovered a jewel-shaped geometric object that challenges the notion that space and time are fundamental constituents of nature.

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.