What's up in

mathematics

Illustration showing a large multicolored graph on top and a smaller one below, which is rising and growing bigger
combinatorics

Disorder Persists in Larger Graphs, New Math Proof Finds

November 4, 2020

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.

Harvard professor L. Mahadevan stands in a slightly cluttered office, holding an apple and a jar containing a miniature brain
Q&A

A Scientist Who Delights in the Mundane

October 26, 2020

From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.

A visualization of the tower formed by the 3-adic numbers
Abstractions blog

An Infinite Universe of Number Systems

October 19, 2020

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.

insights puzzle

Celebrating the Playful Magic of John Horton Conway

October 15, 2020

Have fun exploring a numerical puzzle, a geometric puzzle and a game of random patterns, all inspired by the playful genius of the legendary mathematician.

An illustration of computer scientists looking down a new road that breaks open a traveling salesperson route.
algorithms

Computer Scientists Break Traveling Salesperson Record

October 8, 2020

After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

Illustration of researchers building and writing a digital library, which helps a humanoid robot do advanced math
foundations of mathematics

Building the Mathematical Library of the Future

October 1, 2020

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

Quantized Academy

The Simple Math Problem We Still Can’t Solve

September 22, 2020

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

Photo of students sitting at desks competing in the International Mathematical Olympiad
Abstractions blog

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

September 21, 2020

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

Aerial image of a complicated road network.
Abstractions blog

A New Algorithm for Graph Crossings, Hiding in Plain Sight

September 15, 2020

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.