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# Mathematics

## Latest Articles

### Mathematicians Eliminate Long-Standing Threat to Knot Conjecture

A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.

### Mathematicians Find an Infinity of Possible Black Hole Shapes

In three-dimensional space, the surface of a black hole must be a sphere. But a new result shows that in higher dimensions, an infinite number of configurations are possible.

### The Basic Algebra Behind Secret Codes and Space Communication

Whether you’re passing secret notes in class or downloading images from a space probe, Reed-Solomon codes offer an ingenious way to embed information and correct for errors.

### Mathematicians Roll Dice and Get Rock-Paper-Scissors

Mathematicians have uncovered a surprising wealth of rock-paper-scissors-like patterns in randomly chosen dice.

### Finally, a Fast Algorithm for Shortest Paths on Negative Graphs

Researchers can now find the shortest route through a network nearly as fast as theoretically possible, even when some steps can cancel out others.

### Probability and Number Theory Collide — in a Moment

Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories.

### Google Researcher, Long Out of Math, Cracks Problem About Sets

On nights and weekends, Justin Gilmer attacked an old question in pure math using the tools of information theory.

### The Year in Math

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

### ‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.