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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.

A rectangle broken up into five fractions.
number theory

Math’s ‘Oldest Problem Ever’ Gets a New Answer

By Jordana Cepelewicz
March 9, 2022
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A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

Multimedia

The Map of Mathematics

By Kevin Hartnett
February 13, 2020
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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Insights puzzle

Solution: ‘The Fabulously Fair Feast’

By Pradeep Mutalik
December 22, 2015
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The solution to this month’s puzzle explains how to design a Sudoku square to figure out the likes and dislikes of four or eight finicky friends.

Insights puzzle

The Fabulously Fair Feast

By Pradeep Mutalik
December 10, 2015
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For this month’s puzzle, design a Sudoku square to figure out the likes and dislikes of four finicky friends.

Insights puzzle

Solution: ‘Be Still My Pulsating Sequence’

By Pradeep Mutalik
November 25, 2015
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The solution to this month’s puzzle explains how to find a rule behind a given sequence of numbers and challenges readers to take on a ‘lovely’ unsolved problem.

Insights puzzle

Be Still My Pulsating Sequence

By Pradeep Mutalik
November 12, 2015
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Can you infer the simple rule behind a number sequence that spikes up and down like the beating of a heart?

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