Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the ...

This paper concerns the location of roots of polynomials with respect to the principal coordinate axes (referred to generally as the Routh-Hurwitz criteria and the Sturm criteria). It provides a new ...

His secret is in generalizing two roots together instead of keeping them as separate values. Quadratic equations are polynomials that include an x², and teachers use them to teach students to find two ...