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Mathematics

A photograph of the mathematician James Maynard outside his home in Oxford, England.
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A Number Theorist Who Solves the Hardest Easy Problems

July 1, 2020

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

Animated illustration showing vulnerable red shapes become “infected” and turn green, amid immune blue shapes.
Abstractions blog

The Tricky Math of Herd Immunity for COVID-19

June 30, 2020

Herd immunity differs from place to place, and many factors influence how it’s calculated.

Animation of different rectangles made by connecting four points on a colorful loop.
geometry

New Geometric Perspective Cracks Old Problem About Rectangles

June 25, 2020

While locked down due to COVID-19, Joshua Greene and Andrew Lobb figured out how to prove a version of the “rectangular peg problem.”

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.