Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links ...

For a game whose rules can be taught to a small child, chess is bewilderingly complicated—there are more possible games of chess than there are atoms in the observable universe, and despite the ...

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Zheng Xiao received his PhD in 2022 at Michigan State University, under the supervision of Aaron D. Levin. His research interests include number theory, arithmetic geometry and complex hyperbolic ...

Two-dimensional hyperbolic topological pumping can emulate eight-dimensional quantum Hall physics, transcending conventional dimensional constraints. Furthermore, hyperbolic pumping trajectories are ...

Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can. One such person was mathematician ...

An apple may not fall far from the tree, but for a leaf, it depends on its shape. Elm or apple leaves — oval and symmetrical, with few protruding lobes — fall quickly, making them likely to end up ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...