# Kevin Hartnett

## The Tricky Translation of Mathematical Ideas

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

## 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.

## How to Use a Sphere to Talk to Mars

To avoid garbled messages, mathematicians might translate them into geometric form.

## 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.

## 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.

## 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.

## How Curvature Makes a Shape a Shape

The ancient study of an object’s curvature is guiding mathematicians toward a new understanding of simple equations.

## Test Your Mathematical Sculpting Skills

Can you turn a two-dimensional fractal into a 3-D object? Break out your scissors and tape for a chance to win a 3-D printed sculpture.

## The Math That’s Too Difficult for Physics

How do physicists reconstruct what really happened in a particle collision? Through calculations that are so challenging that, in some cases, they simply can’t be done. Yet.