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Mathematics

Illustration of mathematicians descending through a cavern whose walls are lined with polynomials.
polynomials

Mathematicians Resurrect Hilbert’s 13th Problem

January 14, 2021

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections.

Quantized Academy

The Crooked Geometry of Round Trips

January 13, 2021

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?

An animation showing chaotic swirls of purple coalesce into a single line
Abstractions blog

New Quantum Algorithms Finally Crack Nonlinear Equations

January 5, 2021

Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.

number theory

How I Learned to Love and Fear the Riemann Hypothesis

January 4, 2021

A number theorist recalls his first encounter with the Riemann hypothesis and breaks down the math in a new Quanta video.

2020 in Review

Our Favorite Comments of the Year

Online comment platforms can bring out the best — and the worst — in people. At the end of a tumultuous year, Quanta’s editors highlight some of our favorite things you had to say.

2020 in Review

The Year in Math and Computer Science

December 23, 2020

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

December 16, 2020

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

Abstractions blog

How the Slowest Computer Programs Illuminate Math’s Fundamental Limits

December 10, 2020

The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.

Illustration of a black goat with a red leash, grazing at the intersection of two circles
geometry

After Centuries, a Seemingly Simple Math Problem Gets an Exact Solution

December 9, 2020

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.