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geometry

Abstractions blog

How Randomness Can Make Math Easier

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

geometry

Random Surfaces Hide an Intricate Order

Mathematicians have proved that a random process applied to a random surface will yield consistent patterns.

Q&A

A Mathematician Whose Only Constant Is Change

Amie Wilkinson searches for exotic examples of the mathematical structures that describe change.

Art for "How Geometry, Data and Neighbors Predict Your Favorite Movies"
Quantized Academy

How Geometry, Data and Neighbors Predict Your Favorite Movies

A little high school geometry can help you understand the basic math behind movie recommendation engines.

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 "Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize"
Abel Prize

Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

geometry

Math Duo Maps the Infinite Terrain of Minimal Surfaces

A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.

Art for "Möbius Strips Defy a Link With Infinity"
topology

Möbius Strips Defy a Link With Infinity

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"
geometry

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.