As is usual with these kinds of "structure theorems" (as they're often called), we need to precisely define what set of things we seek to express.

A function which solves a quintic is reasonably ordinary. We can readily compute it to arbitrary precision using any number of methods, just as we can do with square roots or cosines. Not just the quintic, but any polynomial with rational coefficients can be solved. But the solutions can't be expressed with a finite number of draws from a small repertoire of functions like {+, -, *, /}.

So the question is, does admitting a new function into our "repertoire" allow us to express new things? That's what a structure theorem might tell us.

The blog post is exploring this question: Does a repertoire of just the EML function, which has been shown by the original author to be able to express a great variety of functions (like + or cosine or ...) also allow us to express polynomial roots?