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Banach-Tarski and the Paradox of Infinite Cloning
One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces.
Neither Star nor Planet: A Strange Brown Dwarf Puzzles Astronomers
Brown dwarfs such as “The Accident” are illuminating the murky borderlands that separate planets from stars.
Galois Groups and the Symmetries of Polynomials
By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.
The ‘Weirdest’ Matter, Made of Partial Particles, Defies Description
Theorists are in a frenzy over “fractons,” bizarre, but potentially useful, hypothetical particles that can only move in combination with one another.
How Bell’s Theorem Proved ‘Spooky Action at a Distance’ Is Real
The root of today’s quantum revolution was John Stewart Bell’s 1964 theorem showing that quantum mechanics really permits instantaneous connections between far-apart locations.
How ‘Long COVID’ Keeps Us Sick
Other diseases with long-term symptoms can help us understand how COVID can affect us long after the virus itself is gone.
Brighter Than a Billion Billion Suns: Gamma-Ray Bursts Continue to Surprise
These ultrabright flashes have recently been tracked for days, upending ideas about the cataclysms that create them.
How Animals Color Themselves With Nanoscale Structures
Animals sculpt the optical properties of their tissues at the nanoscale to give themselves “structural colors.” New work is piecing together how they do it.
How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.