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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.