What Are Algebraic Curves?

A curve is a one-dimensional object that sits in a higher dimensional space. In the 1870s, mathematicians Alexander von Brill and Max Noether formulated a prediction using only three properties. The genus, or number of holes it has, the degree, or its twistiness, and the number of dimensions that the curve lives in are known as G, D, and R. A new solution to the interpolation problem builds on work from the 19th century.