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# Abstractions blog

## Latest Articles

### To Learn More Quickly, Brain Cells Break Their DNA

New work shows that neurons and other brain cells use DNA double-strand breaks, often associated with cancer, neurodegeneration and aging, to quickly express genes related to learning and memory.

### 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.

### Computer Scientists Discover Limits of Major Research Algorithm

The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult computational problem.

### Physicists Create a Bizarre ‘Wigner Crystal’ Made Purely of Electrons

The unambiguous discovery of a Wigner crystal relied on a novel technique for probing the insides of complex materials.

### Turing Patterns Turn Up in a Tiny Crystal

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.

### 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.

### Proof Assistant Makes Jump to Big-League Math

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