# Kevin Hartnett

## In Topology, When Are Two Shapes the Same?

As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.

## Mathematicians Answer Old Question About Odd Graphs

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

## Undergraduate Math Student Pushes Frontier of Graph Theory

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

## Inside the Secret Math Society Known Simply as Nicolas Bourbaki

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.

## At the Math Olympiad, Computers Prepare to Go for the Gold

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

## Computer Scientists Attempt to Corner the Collatz Conjecture

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

## How Physics Found a Geometric Structure for Math to Play With

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about.

## The Tricky Math of Herd Immunity for COVID-19

Herd immunity differs from place to place, and many factors influence how it’s calculated.

## The ‘Useless’ Perspective That Transformed Mathematics

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

## In Mathematics, It Often Takes a Good Map to Find Answers

Mathematicians try to figure out when problems can be solved using current knowledge—and when they have to chart a new path instead.