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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.
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.
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?
New Proof Shows That ‘Expander’ Graphs Synchronize
The proof establishes new conditions that cause connected oscillators to sway in sync.
Math Patterns That Go On Forever but Never Repeat
Simple math can help explain the complexities of the newly discovered aperiodic monotile.
Is Perpetual Motion Possible at the Quantum Level?
A new phase of matter called a “time crystal” plays with our expectations of thermodynamics. The physicist Vedika Khemani talks with Steven Strogatz about its surprising quantum behavior.
Why the Brain’s Connections to the Body Are Crisscrossed
In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.
A New Symmetry Shakes Up Physics
So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.