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# Mathematics

## Latest Articles

###
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.

### How Can Infinitely Many Primes Be Infinitely Far Apart?

Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be.

### Hypergraphs Reveal Solution to 50-Year-Old Problem

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

### How Do Mathematicians Know Their Proofs Are Correct?

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.