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Mathematics

Abstractions blog

How to Use a Sphere to Talk to Mars

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

Icosahedron
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.

Illustration of a salamander
applied math

How to Quantify (and Fight) Gerrymandering

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.

Illustration: diver searching for new math
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.

Thomas Royen at his home in Schwalbach am Taunus, Germany.
statistics

A Long-Sought Proof, Found and Almost Lost

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

Illustration: Yves Meyer and his wavelet
Abstractions blog

Yves Meyer, Wavelet Expert, Wins Abel Prize

The French mathematician was cited “for his pivotal role in the development of the mathematical theory of wavelets.”

Abstractions blog

19 Women Leading Math and Physics

Top women in mathematics and physics discuss how they got to where they are — and why there aren’t more of them.

Abstractions blog

The Almost-Proof of Fermat’s Last Theorem

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

Colorful illustration of 5 plants with their roots exposed. Each plant forms the shape of a number,
number theory

New Number Systems Seek Their Lost Primes

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.