[waqf]

You are right but I don't think the audience here (people trying to learn Galois theory for the first time) will understand your comment either. The original paper didn't even make clear that a_i are the coefficients and x_i are the roots … that's the level at which we need to be clarifying.

[ky3]

The HN audience isn't the intended audience for this paper by Stillwell, who wrote for other math profs like himself.

To members of HN audience who want to learn GT, I recommend the freely available book by Postnikov.

p.s. Fwiw, the paper did make clear the distinction between the a_i, x_i, and the alpha_i. See the second page proper of TFA.