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geometry
Quantized Columns
The Sordid Past of the Cubic Formula
The quest to solve cubic equations led to duels, betrayals — and modern mathematics.
topology
Special Surfaces Remain Distinct in Four Dimensions
For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.
topology
Unimaginable Surfaces Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
geometry
Father-Son Team Solves Geometry Problem With Infinite Folds
The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.
geometry
An Ancient Geometry Problem Falls to New Mathematical Techniques
Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.
Quantized Academy
Why Triangles Are Easy and Tetrahedra Are Hard
The triangle angle sum theorem makes working with triangles easy. What happens when you can’t rely on it?
2021 in Review
The Year in Math and Computer Science
Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.
geometry
Mathematicians Transcend Geometric Theory of Motion
More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.
Q&A
The Mathematician Who Delights in Building Bridges
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.