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Mathematics

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topology

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

By Kevin Hartnett
October 26, 2021
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Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

an animation showing wavelets at different scales travel across a space
applied math

How Wavelets Allow Researchers to Transform, and Understand, Data

By Alexander Hellemans
October 13, 2021
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Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

A GIF of ice melting in a glass of water
mathematical physics

Mathematicians Prove Melting Ice Stays Smooth

By Mordechai Rorvig
October 6, 2021
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After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.

Illustration showing yellow and green shapes over a blue background
topology

In Topology, When Are Two Shapes the Same?

By Kevin Hartnett
September 28, 2021
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As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

Quantized Academy

The Simple Math Behind the Mighty Roots of Unity

By Patrick Honner
September 23, 2021
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Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

combinatorics

Mathematician Answers Chess Problem About Attacking Queens

By Leila Sloman
September 21, 2021
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The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.

number theory

How Ancient War Trickery Is Alive in Math Today

By Lakshmi Chandrasekaran
September 14, 2021
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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
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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.


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