# Kevin Hartnett

## Three Decades Later, Mystery Numbers Explained

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

## Robert Langlands, Mathematical Visionary, Wins the Abel Prize

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.

## How Einstein Lost His Bearings, and With Them, General Relativity

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

## The Simple Algorithm That Ants Use to Build Bridges

Even with no one in charge, army ants work collectively to build bridges out of their bodies. New research reveals the simple rules that lead to such complex group behavior.

## What Makes the Hardest Equations in Physics So Difficult?

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.

## Mathematicians Crack the Cursed Curve

A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.

## Artificial Intelligence Learns to Learn Entirely on Its Own

A new version of AlphaGo needed no human instruction to figure out how to clobber the best Go player in the world—itself.

## Visionary Mathematician Vladimir Voevodsky Dies at 51

Voevodsky’s friends remember him as constitutionally unable to compromise on the truth—a quality that led him to produce some of the most important mathematics of the 20th century.

## The Math That Promises to Make the World Brighter

The color of LED lights is controlled by a clumsy process. A new mathematical discovery may make it easier for us to get the hues we want.

## Why Mathematicians Like to Classify Things

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.