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In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere
High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.
A Brief History of Tricky Mathematical Tiling
The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.
Biophysicists Uncover Powerful Symmetries in Living Tissue
After identifying interlocking symmetries in mammalian cells, scientists can describe some tissues as liquid crystals — an observation that lays the groundwork for a fluid-dynamic theory of how tissues move.
The Mathematician Who Sculpted the Shape of Space
Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.
Echoes of Electromagnetism Found in Number Theory
A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.
How Simple Math Moves the Needle
The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.
Mathematicians Cross the Line to Get to the Point
A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.
Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
A Tower of Conjectures That Rests Upon a Needle
On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.