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Mathematics

Latest Articles

Illustration of thumbs flipping coins.
information theory

How Shannon Entropy Imposes Fundamental Limits on Communication

By Kevin Hartnett
September 6, 2022
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What’s a message, really? Claude Shannon recognized that the elemental ingredient is surprise.

Quantized Columns

How Isaac Newton Discovered the Binomial Power Series

By Steven Strogatz
August 31, 2022
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Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.

algebraic geometry

Old Problem About Mathematical Curves Falls to Young Couple

By Jordana Cepelewicz
August 25, 2022
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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.

Insights puzzle

Help Star Trek’s Lieutenant Uhura Overcome Astronomical Odds

By Pradeep Mutalik
August 18, 2022
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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.

number theory

A Numerical Mystery From the 19th Century Finally Gets Solved

By Leila Sloman
August 15, 2022
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Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

An illustration of a large, 3D equation that almost looks like a sculpture (that is being inspected by different people, and is surrounded by different numbers and measuring equipment such as rulers and protractors. The equation is x2 − dy2 = –1).
number theory

Mathematicians Crack a Simple but Stubborn Class of Equations

By Jordana Cepelewicz
August 10, 2022
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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.

An illustration with a black disc in the middle evoking a black hole.
mathematical physics

At Long Last, Mathematical Proof That Black Holes Are Stable

By Steve Nadis
August 4, 2022
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The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

Insights puzzle

Seeking Mathematical Truth in Counterfeit Coin Puzzles

By Pradeep Mutalik
July 29, 2022
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Readers balanced logical reasoning and mathematical insights to find phony coins with a double-pan balance scale.

A deltoid and other mathematical shapes.
geometry

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

By Kevin Hartnett
July 26, 2022
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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.


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