polynomials
Mathematicians Find Long-Sought Building Blocks for Special Polynomials
Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.
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.