A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known ...

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 ...

Forbes contributors publish independent expert analyses and insights. I write about the future of learning, work and human development. Okay, we cut a bad deal 20 years ago and it’s time to fix it.

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 ...

Matrix polynomials and moment problems are significant areas of study in mathematics, particularly in the fields of control theory, numerical analysis, and probability. Matrix polynomials are ...

In 2015, the poet-turned-mathematician June Huh helped solve a problem posed about 50 years earlier. The problem was about complex mathematical objects called “matroids” and combinations of points and ...

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work. My recent story for Quanta explained a newly proved ...

How many times during your educational career have you thought to yourself, “When on earth am I ever -- and I mean ever -- going to use this?” I would venture to guess we’ve all thought this a time or ...