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Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
Math Proof Draws New Boundaries Around Black Hole Formation
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.
The Simple Geometry That Predicts Molecular Mosaics
By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.
New Proof Finds the ‘Ultimate Instability’ in a Solar System Model
For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.
How to Tame the Infinities Hiding in the Heart of Particle Physics
In the math of particle physics, every calculation should result in infinity. The set of techniques known as “resurgence” points toward an escape.
New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’
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.
Mathematicians Find an Infinity of Possible Black Hole Shapes
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.