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symmetry

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A Brief History of Tricky Mathematical Tiling

By David S. Richeson
October 30, 2023
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The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

An illustration of a sheet of cells, each with sixfold rotational symmetry. Markings outline that symmetry in a handful of individual cells. Within the tissue, cells also exhibit a higher-order twofold symmetry that emerges at more zoomed-out scales and is indicated by different colors.
biophysics

Biophysicists Uncover Powerful Symmetries in Living Tissue

By Elise Cutts
October 25, 2023
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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.

Langlands program

Echoes of Electromagnetism Found in Number Theory

By Kevin Hartnett
October 12, 2023
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A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

number theory

Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

By Jordana Cepelewicz
September 21, 2023
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Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

graph theory

New Proof Shows That ‘Expander’ Graphs Synchronize

By Leila Sloman
July 24, 2023
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The proof establishes new conditions that cause connected oscillators to sway in sync.

Quantized Academy

Math Patterns That Go On Forever but Never Repeat

By Patrick Honner
May 23, 2023
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Simple math can help explain the complexities of the newly discovered aperiodic monotile.

The Joy of Why

Is Perpetual Motion Possible at the Quantum Level?

By Steven Strogatz
May 3, 2023
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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.

Quantized Columns

Why the Brain’s Connections to the Body Are Crisscrossed

By R. Douglas Fields
April 19, 2023
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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.

mathematical physics

A New Symmetry Shakes Up Physics

By Kevin Hartnett
April 18, 2023
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So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.


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