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# Mathematics

## Latest Articles

### A New 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.

### Is There Math Beyond the Equal Sign?

Can mathematics handle things that are essentially the same without being exactly equal? Category theorist Eugenia Cheng and host Steven Strogatz discuss the power and pleasures of abstraction.

### Surprise Computer Science Proof Stuns Mathematicians

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

### Coloring by Numbers Reveals Arithmetic Patterns in Fractions

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.