Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...

We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...

All products featured on WIRED are independently selected by our editors. However, we may receive compensation from retailers and/or from purchases of products through these links. Adding to his ...

We show that the binary expansions of algebraic numbers do not form secure pseudorandom sequences; given sufficiently many initial bits of an algebraic number, its minimal polynomial can be ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

A mathematician has solved a 200-year-old maths problem after figuring out a way to crack higher-degree polynomial equations without using radicals or irrational numbers. The method developed by ...

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials: \(6{x^5} - 3{x^2} + 7\) is a polynomial ...