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geometry

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

Marjorie Rice’s Secret Pentagons

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

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

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.

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

How to Use a Sphere to Talk to Mars

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

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.
geometry

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.

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

Quantum Questions Inspire New Math

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

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

A Long-Sought Proof, Found and Almost Lost

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

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

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.

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.
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.

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.
Abstractions blog

How Curvature Makes a Shape a Shape

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.