(edit: hang on, am I crazy or do these bagels look remarkably similar? despite very different definitions)
From Giulio Tiozzo
"Of course, the similarity between the set of zeros of Littlewood polynomials and Thurston’s entropy bagel is striking.
In fact, I proved a few years ago that the two fractal sets the same inside the unit disk!
The difference is that Baez’s set is symmetric under circle inversion, while Thurston’s set is not: the parts outside of the unit disk are completely different."
The fact that they look similar is striking. It means in some sense roots of integer polynomials generate more complex iterative systems, which is surprising (to me).
> A number is totally real if it satisfies a polynomial equation with integer coefficients that only has real roots.
Nothing wrong with that.
See: https://en.wikipedia.org/wiki/Totally_real_number_field
Added: in fact the Quanta article gets this right. It says "A number is totally real if it satisfies a polynomial equation with integer coefficients that only has real roots." Also, Jordana Cepelowicz is a knowledgeable math writer and I believe she has a PhD in math.
For instance, 'i' is algebraic but not totally real (it isn't a real number!), since it satisfies 'x^2 + 1'.
Any popularization is inevitably going to run into some inaccuracies—or else it's just re-publishing the technical papers—but the opinions of most mathematicians I know are that, far from being garbage, Quanta's reporting is distinctly better than most.