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Illustration showing an austere number line on one side and various interesting objects on the the other, including a dodecahedron, an armillary sphere, flowers and plants.
Quantized Columns

The Two Forms of Mathematical Beauty

June 16, 2020

Mathematicians typically appreciate either generic or exceptional beauty in their work, but one type is more useful in describing the universe.

Diagram showing a colorful visualization of the simple Lie group
Abstractions blog

The ‘Useless’ Perspective That Transformed Mathematics

June 9, 2020

Representation theory was initially dismissed. Today, it’s central to much of mathematics.

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

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

May 14, 2020

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.