In the 1800s, prior to Hilbert’s list of problems, mathematicians discovered that the roots of unity could serve as “building blocks” for the particular collection of numbers that they wanted to study ...

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 ...

Quadratic equations are polynomials, meaning strings of math terms. An expression like “x + 4” is a polynomial. They can have ...

We study the distribution of the complex roots of random polynomials of degree n with i.i.d. coefficients. Using techniques related to Rice's treatment of the real roots question, we derive, under ...

The roots of x2 – 5 = 0 help solve lots of other equations in our mathematical system, like x2 – 20 = 0. (Note that here, our mathematical system is limited to polynomials and rational numbers.) But ...