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mathematics

Q&A

A ‘Rebel’ Without a Ph.D.

A conversation with the mathematical physicist Freeman Dyson on quantum electrodynamics, climate change and his latest pet project.

Submerged turbulent jet
Mathematics

A Fluid New Path in Grand Math Challenge

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow.

Photograph of Saturn and its moons.
Mathematics

A New Tool to Help Mathematicians Pack

Improvements in how densely spheres and other shapes can be packed together could lead to advances in materials science, deep space communication and theoretical physics.

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.
Mathematics

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.