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# Mathematics

## Latest Articles

### Why Mathematicians Re-Prove What They Already Know

It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

### The Number 15 Describes the Secret Limit of an Infinite Grid

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

### How Can Some Infinities Be Bigger Than Others?

All infinities go on forever, so how is it possible for some infinities to be larger than others? The mathematician Justin Moore discusses the mysteries of infinity with Steven Strogatz.

### A New Kind of Symmetry Shakes Up Physics

So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.

### Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

### Hobbyist Finds Math’s Elusive ‘Einstein’ Tile

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

### The Colorful Problem That Has Long Frustrated Mathematicians

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

### Emmy Murphy Is a Mathematician Who Finds Beauty in Flexibility

The prize-winning geometer feels most fulfilled when exploring the fertile ground where constraint meets creation.

### The Symmetry That Makes Solving Math Equations Easy

Learn why the quadratic formula works and why quadratics are easier to solve than cubics.