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.
So an app that would probably serve a real need fails because the team is unable to bootstrap the two-sided market. The best dev moves to a bullshit "green habits" app that doesn't suffer from such problems because... it doesn't really do much in the first place. Not the greatest outcome for the world.
Don't you remember before inflation when we were able to focus on climate change!
But you totally got us there, the startup failed because we were a vitamin (and because our on-the-fence seed round was scuppered by Putin cooling some feet)
true, it wouldn't do a 100% job, but it would be another line of defense. the reason I was wondering about it was that the gp cited an example that was easy for humans to miss, but would be caught at once with a spell checker.
there are also statistical methods to detect words that are changed into other, valid words - check out the grammar checker in google docs for instance. again, not 100%, but every bit helps.
It would probably also throw out a lot of false positives which would take time to check. Especially in works of fiction, writers could take liberties with non-standard spelling.
