Cash for Math: The Erdős Prizes Live On
Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.
A Puzzle of Clever Connections Nears a Happy End
The three young friends who devised the “happy ending” problem would become some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle. Now it receives its first big breakthrough.
A Simple Visual Proof of a Powerful Idea
Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.
How to Use a Sphere to Talk to Mars
To avoid garbled messages, mathematicians might translate them into geometric form.
A New Path to Equal-Angle Lines
Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.
The Almost-Proof of Fermat’s Last Theorem
19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.
New Number Systems Seek Their Lost Primes
For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.
The Hidden Twist to Making a Möbius Strip
The simple Möbius strip illustrates a deep mathematical challenge that has long tormented the field of symplectic geometry.
A Fight to Fix Geometry’s Foundations
When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry.