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Art for "How Feynman Diagrams Revolutionized Physics"
sphere packing

Out of a Magic Math Function, One Solution to Rule Them All

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

Art for "Scientists Discover Exotic New Patterns of Synchronization"

Scientists Discover Exotic New Patterns of Synchronization

In a world seemingly filled with chaos, physicists have discovered new forms of synchronization and are learning how to predict and control them.

Art for "A Proof About Where Symmetries Can’t Exist"

A Proof About Where Symmetries Can’t Exist

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Art for "Three Decades Later, Mystery Numbers Explained"
Abstractions blog

Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Illustration for "Mathematicians Explore Mirror Link Between Two Geometric Worlds"

Mathematicians Explore Mirror Link Between Two Geometric Worlds

Decades after physicists happened upon a stunning mathematical coincidence, researchers are getting close to understanding the link between two seemingly unrelated geometric universes.

Jennifer Balakrishnan and Sachi Hashimoto, plotted using SageMath
Abstractions blog

Mathematicians Crack the Cursed Curve

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

Minhyong Kim in front of a whiteboard
number theory

Secret Link Uncovered Between Pure Math and Physics

An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.

Pariah moonshine
number theory

Mathematicians Find Moonshine Link for Pariah Symmetries

A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.

fidget spinners
Quantized Academy

Symmetry, Algebra and the Monster

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.