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Mathematics

patterns

Turing Patterns Turn Up in a Tiny Crystal

By Elena Renken
August 10, 2021
Read Later

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.

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.

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.

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.

Quantized Academy

How to Find Rational Points Like Your Job Depends on It

By Patrick Honner
July 22, 2021
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Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

Illustration showing geometric figures at left connected via wormhole to numbers at right.
Langlands program

New Shape Opens ‘Wormhole’ Between Numbers and Geometry

By Kevin Hartnett
July 19, 2021
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Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.

foundations of mathematics

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

By Natalie Wolchover
July 15, 2021
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For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.

A pixelated black and white animation of a model of percolation.
mathematical physics

Mathematicians Prove Symmetry of Phase Transitions

By Allison Whitten
July 8, 2021
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A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

Insights puzzle

Can Math Help You Escape a Hungry Bear?

By Pradeep Mutalik
June 29, 2021
Read Later

In this month’s puzzle, math is a question of life or death.


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