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How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
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.
How Wavelets Allow Researchers to Transform, and Understand, Data
Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.
Mathematicians Prove Melting Ice Stays Smooth
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.
In Topology, When Are Two Shapes the Same?
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.
The Simple Math Behind the Mighty Roots of Unity
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.
Mathematician Answers Chess Problem About Attacking Queens
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.
How Ancient War Trickery Is Alive in Math Today
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.
The Journey to Define Dimension
The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.
New Math Book Rescues Landmark Topology Proof
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.