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geometry

Animation showing two sets of tangrams cycling between identical squares and different shapes.
geometry

Mathematicians Cut Apart Shapes to Find Pieces of Equations

October 31, 2019

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

foundations of mathematics

With Category Theory, Mathematics Escapes From Equality

October 10, 2019

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

Abstractions blog

How Randomness Can Make Math Easier

July 9, 2019

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

July 2, 2019

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

June 13, 2019

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

May 22, 2019

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

May 13, 2019

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

March 19, 2019

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

March 12, 2019

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.