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Mathematicians Solve Decades-Old Classification Problem

August 5, 2021

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

Neither Star nor Planet: A Strange Brown Dwarf Puzzles Astronomers

August 4, 2021

Brown dwarfs such as “The Accident” are illuminating the murky borderlands that separate planets from stars.

Galois Groups and the Symmetries of Polynomials

August 3, 2021

By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Mating Contests Among Females, Long Ignored, May Shape Evolution

August 2, 2021

Showy male competitions over mating privileges have grabbed scientists’ attention more often, but new work hints that sexual selection is also widespread among females.

Eternal Change for No Energy: A Time Crystal Finally Made Real

July 30, 2021

Like a perpetual motion machine, a time crystal forever cycles between states without consuming energy. Physicists claim to have built this new phase of matter inside a quantum computer.

Proof Assistant Makes Jump to Big-League Math

July 28, 2021

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

A Soil-Science Revolution Upends Plans to Fight Climate Change

July 27, 2021

A centuries-old concept in soil science has recently been thrown out. Yet it remains a key ingredient in everything from climate models to advanced carbon-capture projects.

The ‘Weirdest’ Matter, Made of Partial Particles, Defies Description

July 26, 2021

Theorists are in a frenzy over “fractons,” bizarre, but potentially useful, hypothetical particles that can only move in combination with one another.

How to Find Rational Points Like Your Job Depends on It

July 22, 2021

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

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