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# Geometry

## Latest Articles

### The Beautiful Mathematical Explorations of Maryam Mirzakhani

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

### Marjorie Rice’s Secret Pentagons

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.

### Pentagon Tiling Proof Solves Century-Old Math Problem

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

### How to Use a Sphere to Talk to Mars

To avoid garbled messages, mathematicians might translate them into geometric form.

### A New Path to Equal-Angle Lines

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

### Quantum Questions Inspire New Math

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

### A Long-Sought Proof, Found and Almost Lost

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

### The Hidden Twist to Making a Möbius Strip

The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.

### A Fight to Fix Geometry’s Foundations

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.