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Abstractions blog

How the Slowest Computer Programs Illuminate Math’s Fundamental Limits

December 10, 2020

The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.

Illustration of a black goat with a red leash, grazing at the intersection of two circles

After Centuries, a Seemingly Simple Math Problem Gets an Exact Solution

December 9, 2020

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.


The Computer Scientist Who Shrinks Big Data

December 7, 2020

Jelani Nelson designs clever algorithms that only have to remember slivers of massive data sets. He also teaches kids in Ethiopia how to code.

Photo of Ashwin Sah standing in front of a sculpture in a park
Abstractions blog

Undergraduate Math Student Pushes Frontier of Graph Theory

November 30, 2020

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

insights puzzle

How to Solve Our Three John Conway-Inspired Puzzles

November 20, 2020

A numerical puzzle, a geometric puzzle and a game of random patterns — all with connections to the legendary mathematician — elicited an enthusiastic response from readers.

Graphical model of a cubic earth.

Scientists Uncover the Universal Geometry of Geology

November 19, 2020

An exercise in pure mathematics has led to a wide-ranging theory of how the world comes together.

Quantized Academy

Some Math Problems Seem Impossible. That Can Be a Good Thing.

November 18, 2020

Struggling with math problems that can’t be solved helps us better understand the ones we can.


Searching Symbols for the Rules of Change

November 17, 2020

Bryna Kra searches for the patterns in sequences of numbers that explain how complicated dynamical systems evolve over time.

computer security

Computer Scientists Achieve ‘Crown Jewel’ of Cryptography

November 10, 2020

A cryptographic master tool called indistinguishability obfuscation has for years seemed too good to be true. Three researchers have figured out that it can work.