So talking about eugenics in a positive way equals racist commentary?
I have a genetic mutation (de novo) that leads to a disability and that I don't want to pass on. Natural approach: Die, due to the lack of therapeutic modalities. No chance of offspring. With the help of medicine, I am alive. Now, to prevent passing on mutated genes but still have children, I could use something like IVF and reproductive genetics. This is textbook eugenics(?)
Obviously I disapprove of the stereotypical eugenics of the century. Ranging from Germans murdering disabled children to Danes forcing Greenland women on birth control.
Tikz is misplaced in this list; it is how you make any kind of vector drawings in LaTeX. It's not the only way, but perhaps the best documented and most expressive one. If you have any such drawings in your work, you won't get around putting some effort into it. Not comparable with boxed theorems or fancy headings.
I think the annoyance with TikZ is twofold: (1) it tries to do a really hard thing (create a picture with text in a human writable way), (2) it is used infrequently enough that it’s hard to learn through occasional use.
That said, nobody makes you use TikZ, fire up Inkscape and do it wysiwyg.
That looks like the kind of paper that causes companies to lose lots of money by hyping up what is likely a less-than-impressive method. But it does not make any theoretical claims, so it cannot contaminate research.
This is about solving polynomial equations using Lagrange inversion. This method, as one might have guessed, is due to... Lagrange. See https://www.numdam.org/item/RHM_1998__4_1_73_0.pdf for a historical survey. What Wildberger is suggesting is a new(?) formula for the coefficients of the resulting power series. Whether it is new I am not sure about -- Wildberger has been working in isolation from others in the field, which is already full of rediscoveries. Note that the method does not compete with solutions in radicals (as in the quadratic formula, Tartaglia, Cardano, del Ferro, Galois) because it produces infinite sums even when applied to quadratic equations.
The (actual) article has a fairly detailed literature review in the introduction, and makes it pretty clear that the main idea was sort-of known already if you squint - but it looks like nobody had put the whole theory together elegantly and advertised it properly. The fact that they couldn't find some natural slices of the hyper-Catalan numbers on OEIS supports that.
The proof they give that the hyper-Catalan series solves the Lagrange inversion problem is very good from a pedagogical point of view - I don't think I'll ever be able to forget it now that I've seen it. The only thing this paper is missing is a direct, self-contained combinatorial proof of the factorial-ratio formula they gave for the hyper-Catalan numbers - digging though the chain of equivalences proved in the references eventually got too annoying for me and I had to sit down and find a proof myself (there is a simple variation of the usual argument for counting Dyck paths [1] that does the trick).
Another thing to note is that the power series solution isn't just "a power series" - it's a hypergeometric series. There are lots of computation techniques that apply to hypergeometric series which don't apply to power series in general (see [2]).
One day, someone will discover a use for across-the-page watermarks that is not better handled by marginalia and makes up for the loss in readability, copyability and compatibility with graphics.
