topology
How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.
combinatorics
Mathematicians Settle Erdős Coloring Conjecture
Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.
number theory
Mathematicians Set Numbers in Motion to Unlock Their Secrets
A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.
Abstractions blog
An Infinite Universe of Number Systems
The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.