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

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

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

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

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

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.

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

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.

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