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mathematical physics

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A modular form is shown as a distorted, rainbow-hued dome atop concentric circles.
number theory

New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

By Jordana Cepelewicz
March 9, 2023
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Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

Fanciful illustration of galaxies with various geometric shapes at their centers.
mathematical physics

Mathematicians Find an Infinity of Possible Black Hole Shapes

By Steve Nadis
January 24, 2023
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In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.

A GIF of a spinning vortex made up of fluid equations
fluid dynamics

Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

By Jordana Cepelewicz
November 16, 2022
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For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

Svetlana Jitomirskaya in a blue shirt with her hands out.
Q&A

A Mathematician Who Fled to Freedom but Still Faces Doubts

By Jordana Cepelewicz
November 1, 2022
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Svetlana Jitomirskaya was born in Ukraine, but left the Soviet Union to escape sexism and antisemitism. Even though her work in mathematical physics has now been honored with one of the field’s top prizes, she finds herself still fighting old battles.

An illustration with a black disc in the middle evoking a black hole.
mathematical physics

At Long Last, Mathematical Proof That Black Holes Are Stable

By Steve Nadis
August 4, 2022
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The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

Illustration of a rotating object that warps the space-time fabric around itself, as seen by eyes located in different places
general relativity

Mass and Angular Momentum, Left Ambiguous by Einstein, Get Defined

By Steve Nadis
July 13, 2022
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Surprising as it may sound, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.

Hugo Duminil-Copin wearing glasses
2022 Fields and Abacus Medals

For His Sporting Approach to Math, a Fields Medal

By Jordana Cepelewicz
July 5, 2022
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With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.

Illustration of a wheel made of motors connected by arms. The wheel is shown in different stretched and squashed configurations.
complex systems

Wheel Made of ‘Odd Matter’ Spontaneously Rolls Uphill

By Ben Brubaker
June 15, 2022
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Physicists have solved a key problem of robotic locomotion by revising the usual rules of interaction between simple component parts.

A ring of bubbles in blue water.
fluid dynamics

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

By Leila Sloman
May 2, 2022
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The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.


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