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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.