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# Algebra

## Latest Articles

### How Isaac Newton Discovered the Binomial Power Series

Rethinking questions and chasing patterns led Newton to find the connection between curves and infinite sums.

### Old Problem About Mathematical Curves Falls to Young Couple

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

### 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.