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Mathematics

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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.

cartoon of a red-headed woman holding a flashlight that illuminates certain numbers against a dark blue background
Quantized Academy

How Can Infinitely Many Primes Be Infinitely Far Apart?

By Patrick Honner
July 21, 2022
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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.

combinatorics

Hypergraphs Reveal Solution to 50-Year-Old Problem

By Leila Sloman
July 14, 2022
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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.

The Joy of Why

How Do Mathematicians Know Their Proofs Are Correct?

By Steven Strogatz
July 13, 2022
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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.

Illustration of a rotating object that warps the space-time fabric around itself, as seen by eyes located in different places
general relativity

Mass and Angular Momentum, Left Ambiguous by Einstein, Get Defined

By Steve Nadis
July 13, 2022
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Surprising as it may sound, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.

2022 Fields and Abacus Medals

A Solver of the Hardest Easy Problems About Prime Numbers

By Erica Klarreich
July 5, 2022
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On his way to winning a Fields Medal, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.


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