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What's up in

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 new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

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.

For this month’s puzzle, design a Sudoku square to figure out the likes and dislikes of four finicky friends.

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.

Can you infer the simple rule behind a number sequence that spikes up and down like the beating of a heart?