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In a Single Measure, Invariants Capture the Essence of Math Objects
To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.
In Mathematics, It Often Takes a Good Map to Find Answers
Mathematicians try to figure out when problems can be solved using current knowledge — and when they have to chart a new path instead.
Symbolic Mathematics Finally Yields to Neural Networks
After translating some of math’s complicated equations, researchers have created an AI system that they hope will answer even bigger questions.
Graduate Student Solves Decades-Old Conway Knot Problem
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.
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.
New Math Proves That a Special Kind of Space-Time Is Unstable
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.
To Win This Numbers Game, Learn to Avoid Math Patterns
Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.
Math After COVID-19
Modern mathematics relies on collaboration and travel. COVID-19 is making it increasingly difficult.
New Earthquake Math Predicts How Destructive They’ll Be
The “pinball” model of a slipping fault line borrows from the mathematics of avalanches.