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Mathematics

An illustration of a knot that mathematicians might study using tools called invariants.
topology

In a Single Measure, Invariants Capture the Essence of Math Objects

June 2, 2020

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

Photo of various colorful maps
Abstractions blog

In Mathematics, It Often Takes a Good Map to Find Answers

June 1, 2020

Mathematicians try to figure out when problems can be solved using current knowledge — and when they have to chart a new path instead.

Illustration of a robot translating calculus into branching, tree-like structures
artificial intelligence

Symbolic Mathematics Finally Yields to Neural Networks

May 20, 2020

After translating some of math’s complicated equations, researchers have created an AI system that they hope will answer even bigger questions.

knot theory

Graduate Student Solves Decades-Old Conway Knot Problem

May 19, 2020

It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.

Photo of iron filings spread along magnetic field lines on a green and yellow background
number theory

Mathematician Measures the Repulsive Force Within Polynomials

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart.

Animation of black hole formation.
mathematical physics

New Math Proves That a Special Kind of Space-Time Is Unstable

May 11, 2020

Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.

Quantized Academy

To Win This Numbers Game, Learn to Avoid Math Patterns

May 7, 2020

Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.

Abstractions blog

Math After COVID-19

April 28, 2020

Modern mathematics relies on collaboration and travel. COVID-19 is making it increasingly difficult.

Black and white photo of John Conway against a black background
Abstractions blog

John Conway Solved Mathematical Problems With His Bare Hands

April 20, 2020

The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.