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patterns

Turing Patterns Turn Up in a Tiny Crystal

By Elena Renken
August 10, 2021
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The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

Photo of crows.
cognitive science

Animals Count and Use Zero. How Far Does Their Number Sense Go?

By Jordana Cepelewicz
August 9, 2021
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Crows recently demonstrated an understanding of the concept of zero. It’s only the latest evidence of animals’ talents for numerical abstraction — which may still differ from our own grasp of numbers.

Illustration of people along a path classifying colorful mathematical trees
set theory

Mathematicians Solve Decades-Old Classification Problem

By Steve Nadis
August 5, 2021
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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.

A dark red planetlike object.
explainers

Neither Star nor Planet: A Strange Brown Dwarf Puzzles Astronomers

By Jonathan O'Callaghan
August 4, 2021
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Brown dwarfs such as “The Accident” are illuminating the murky borderlands that separate planets from stars.

Animated illustration showing multiple permutations of colorful letters
group theory

Galois Groups and the Symmetries of Polynomials

By Allison Whitten
August 3, 2021
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By focusing on relationships between solutions to polynomial equations, rather than the exact solutions themselves, Évariste Galois changed the course of modern mathematics.

Photograph of two female red deer, fighting with their front hooves.
evolution

Mating Contests Among Females, Long Ignored, May Shape Evolution

By Jake Buehler
August 2, 2021
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Showy male competitions over mating privileges have grabbed scientists’ attention more often, but new work hints that sexual selection is also widespread among females.

Animation of a gemstone flipping up and down between mirror-image states.
quantum computing

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

By Natalie Wolchover
July 30, 2021
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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.

Illustration of colorful flowchart using raised blocks against a black background
proofs

Proof Assistant Makes Jump to Big-League Math

By Kevin Hartnett
July 28, 2021
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Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

A cutaway of thick brown soil with grasses on top.
climate science

A Soil-Science Revolution Upends Plans to Fight Climate Change

By Gabriel Popkin
July 27, 2021
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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.


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