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# Mathematics

## Latest Articles

### How Shannon Entropy Imposes Fundamental Limits on Communication

What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.

### How Isaac Newton Discovered the Binomial Power Series

Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.

### Old Problem About Mathematical Curves Falls to Young Couple

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

### Help Star Trek’s Lieutenant Uhura Overcome Astronomical Odds

In honor of the actor and activist Nichelle Nichols, this month’s puzzle imagines a *Star Trek* adventure in which her character, Lieutenant Uhura, faces a life-and-death conundrum.

### A Numerical Mystery From the 19th Century Finally Gets Solved

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

### Mathematicians Crack a Simple but Stubborn Class of Equations

Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.

### At Long Last, Mathematical Proof That Black Holes Are Stable

The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

### Seeking Mathematical Truth in Counterfeit Coin Puzzles

Readers balanced logical reasoning and mathematical insights to find phony coins with a double-pan balance scale.

### A Question About a Rotating Line Helps Reveal What Makes Real Numbers Special

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.