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# algebra

## Latest Articles

### The Sordid Past of the Cubic Formula

The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

### What Is the Langlands Program?

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

### How Infinite Series Reveal the Unity of Mathematics

Infinite sums are among the most underrated yet powerful concepts in mathematics, capable of linking concepts across math’s vast web.

### The Simple Math Behind the Mighty Roots of Unity

Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

### How to Find Rational Points Like Your Job Depends on It

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

### Mathematician Disproves 80-Year-Old Algebra Conjecture

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

### Mathematicians Resurrect Hilbert’s 13th Problem

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

### When Math Gets Impossibly Hard

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

### The ‘Useless’ Perspective That Transformed Mathematics

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