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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.

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.

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

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.

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

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

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.

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.

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.

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