# Explainers

### Decoding Math’s Most Famous Fractal

Mathematicians working in the field of complex dynamical systems are patiently unraveling the Mandelbrot set’s mysteries and may be on the verge of solving a fundamental conjecture that would allow them to describe the set completely.

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### Searching for Dark Matter with a Tabletop ‘Quantum Compass’

The physicist Alex Sushkov has developed one of the most targeted magnetic resonance experiments to date with the aim of detecting a hypothetical dark matter particle called the axion.

### Can Large Language Models Understand ‘Meaning’?

Brown University computer scientist Ellie Pavlick is translating philosophical concepts such as “understanding” and “meaning” into concrete ideas that are testable on LLMs.

### Predicting Eclipses: The Three Body Problem

Solar eclipse prediction has driven innovation across the history of science and mathematics, from the Saros cycle to Greek geometry to Newton’s calculus to the three-body problem.

### Understanding Cryptography With These Five Worlds

Russell Impagliazzo describes the five possible cryptographic worlds we might inhabit.

### Why Is This Basic Computer Science Problem So Hard?

Computer scientists have long used vector addition systems to model how certain programs work, but they didn’t have a full understanding of how complicated they could be. Recent work has finally pinned it down, showing that these problems are far more complicated than they seem.

### How a New X-Ray Technique Sees Black Holes

Astrophysicist Erin Kara explores black holes by carefully tracking the gas and plasma swirling near their event horizons.

### Decoding Math’s Most Famous Fractal

Mathematicians working in the field of complex dynamical systems are patiently unraveling the Mandelbrot set’s mysteries and may be on the verge of solving a fundamental conjecture that would allow them to describe the set completely.

### The Math Hiding in Plain Sight

Sarah Hart, the professor of geometry at Gresham College, sees symmetry everywhere.

### 2023’s Biggest Breakthroughs in Math

In 2023, mathematicians improved bounds on Ramsey numbers, a central measure of order in graphs; found a new aperiodic monotile; and discovered a new upper bound to the size of sets without 3-term arithmetic progressions.