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mathematical physics

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number theory

Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

By Jordana Cepelewicz
September 21, 2023
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Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

mathematical physics

Math Proof Draws New Boundaries Around Black Hole Formation

By Steve Nadis
August 16, 2023
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For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.

An illustration of a honeycomb-shaped molecular mosaic. Formed by a six-sided molecule, the hexagonal mosaic is a pattern within a pattern, with multiple levels of organization.
materials science

The Simple Geometry That Predicts Molecular Mosaics

By Elise Cutts
June 21, 2023
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By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.

The Joy of Why

What Causes Giant Rogue Waves?

By Steven Strogatz
June 14, 2023
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Wave-science researcher Ton van den Bremer and Steven Strogatz discuss how rogue waves can form in relatively calm seas and whether their threat can be predicted.

nonlinear dynamics

New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

By Jordana Cepelewicz
May 16, 2023
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For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

mathematical physics

A New Symmetry Shakes Up Physics

By Kevin Hartnett
April 18, 2023
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So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

mathematical physics

How to Tame the Infinities Hiding in the Heart of Particle Physics

By Charlie Wood
April 6, 2023
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In the math of particle physics, every calculation should result in infinity. The set of techniques known as “resurgence” points toward an escape.

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.


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