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How the Square Root of 2 Became a Number
Useful mathematical concepts, like the number line, can linger for millennia before they are rigorously defined.
The Hidden Connection That Changed Number Theory
Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.
Two Students Unravel a Widely Believed Math Conjecture
Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.
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.
Math’s ‘Oldest Problem Ever’ Gets a New Answer
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.
The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
Solution: ‘The Fabulously Fair Feast’
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.
The Fabulously Fair Feast
For this month’s puzzle, design a Sudoku square to figure out the likes and dislikes of four finicky friends.
Solution: ‘Be Still My Pulsating Sequence’
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.