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# explainers

## Latest Articles

### Vacuum of Space to Decay Sooner Than Expected (but Still Not Soon)

One of the quantum fields that fills the universe is special because its default value seems poised to eventually change, changing everything.

### What Are Sheaves?

These metaphorical gardens have become central objects in modern mathematics.

### What Is Machine Learning?

Neural networks and other forms of machine learning ultimately learn by trial and error, one improvement at a time.

### How the Square Root of 2 Became a Number

Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.

### The Enduring Mystery of How Water Freezes

Making ice requires more than subzero temperatures. The unpredictable process takes microscopic scaffolding, random jiggling and often a little bit of bacteria.

### The S-Matrix Is the Oracle Physicists Turn To in Times of Crisis

Particle physicists in search of the next theory of reality are consulting a mathematical structure that they know will never fail: a table of possibilities known as the S-matrix.

### Computer Scientists Invent an Efficient New Way to Count

By making use of randomness, a team has created a simple algorithm for estimating large numbers of distinct objects in a stream of data.

### How Do Machines ‘Grok’ Data?

By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.

### The Hidden Connection That Changed Number Theory

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.