Mathematics

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.

A two-player game can reveal whether the universe has an infinite amount of complexity.

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

In spite of their name, “imaginary” numbers are as real as any other numbers, especially when it comes to hunting for lost treasure.

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.

Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.

The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.