There is a huge number of people who understand Taylor series, know how to compute them, and the things you can do with Taylor (and other kinds of) expansions. Yet none of us identified that this binary operation spans that lot of them, but I'm willing to read references to predating observations of the same kind. The author does mention alternative systems (incomplete in some specific sense) in the paper.

I did however keep thinking there was a lot of attention to trying to include special constants even though we don't know that much about these constants yet, while comparatively little attention went to say elliptic integrals etc.

When aiming for a wide catch, you'd include some of those esoteric functions, or erf() etc...

I also wished they had attempted to find a representation for derivative and integrals.