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.

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.

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.

A science fiction novelist and an internet commenter made breakthroughs on a longstanding problem about the number of ways you can arrange a set of items. What did they discover?

Several mathematicians under the age of 30 left their marks all over the field, and amateur problem-solvers of all ages made significant contributions to long-dormant puzzles.