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Mathematics

number theory

How Ancient War Trickery Is Alive in Math Today

By Lakshmi Chandrasekaran
September 14, 2021
Read Later

Legend says the Chinese military once used a mathematical ruse to conceal its troop numbers. The technique relates to many deep areas of modern math research.

Quantized Columns

The Journey to Define Dimension

By David S. Richeson
September 13, 2021
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The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
Read Later

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.

An orange ball decomposing into points and rematerializing as two balls, each the same size as the first.
explainers

Banach-Tarski and the Paradox of Infinite Cloning

By Max G. Levy
August 26, 2021
Read Later

One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.

Insights puzzle

Math Can, in Theory, Help You Escape a Hungry Bear

By Pradeep Mutalik
August 25, 2021
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How readers used their geometry skills to survive a dangerous puzzle.

graph theory

How Big Data Carried Graph Theory Into New Dimensions

By Stephen Ornes
August 19, 2021
Read Later

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

patterns

Turing Patterns Turn Up in a Tiny Crystal

By Elena Renken
August 10, 2021
Read Later

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

Illustration of people along a path classifying colorful mathematical trees
set theory

Mathematicians Solve Decades-Old Classification Problem

By Steve Nadis
August 5, 2021
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A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

Animated illustration showing multiple permutations of colorful letters
group theory

Galois Groups and the Symmetries of Polynomials

By Allison Whitten
August 3, 2021
Read Later

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.


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