> What is this [Greek notation] about?

The Greeks "notation" was a diagram full of points labeled by letters (Α, Β, Γ, ...) with various lines connecting them and a list of steps to do with an unmarked ruler and a compass, some of which added new points. But those tools alone can't be used to describe cube roots of arbitrary numbers (or, equivalently, trisections of arbitrary angles).

> What is this [statisticians' function]?

The integral of the bell curve (normal distribution) is called its cumulative distribution function (CDF). The CDF of the normal distribution is closely related to a special function called the "error function" erf(x).

> Is there a good intro to [the symmetry interpretation of the quadratic formula]?

There's some discussion at Wikipedia's article about the quadratic formula: https://en.wikipedia.org/wiki/Quadratic_formula#By_Lagrange_...