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.