alt Hacker News> who claim they have read/studied a) Euclid's Elements
Of the lot, Elements feels misplaced.
Lots of people actually do read Elements as part of their course of study. It's niche but there's a whole cottage industry within academia for that sort of thing. There are probably over a dozen institutions that have either a degree program or a core curriculum that is organized around original texts, with Euclid usually serving as the math distribution of that sequence. So running into people who have read (big chunks of) Elements is not that uncommon. That's true even IRL outside of online discussions forums on thread topics that likely select for such people.
My impression is that this is not really true of the other examples. Except maybe Godel's proofs; I do think a sufficiently motivated instructor could pull a decent chunk of college students through the original text in a semester. Probably better ways to spend everyone's time, though.
Seconding that that one stood out to me. Actually studying at-least large portions of it is typical at a handful of liberal arts colleges that favor the "great books" approach, at least a couple of which have pretty good reputations and are likely to have turned out some folks who work in tech (maybe the programmer next to you... maybe your manager's manager), plus it's pushed in great books home learning programs that surely at least a fair number of people have credibly attempted, even if the overwhelming majority of those who start such programs don't complete them (and it's usually very early in those programs, so even those who gave it a real shot but abandoned it before getting far were likely exposed to quite a bit of Euclid, though maybe they dropped off before On Conic Sections or other texts common in those reading sequences).
... plus it's relatively approachable as such things go, and short enough that closely reading most or all of it isn't a crazy idea, and it was recently-enough widely used as an actual textbook that between that and ongoing modern interest in its use in that capacity, there are tons of study-oriented editions of it floating around and still being published. I mean hell "recreational mathematics" is a thing and lightly-annotated-and-updated Euclid's a pretty solid text for people with that kind of interest to noodle on, with bonus historical appeal since it's super-old and also is assumed background for all educated people into at least the early 20th century, so pops up all the time in historical writing and literature.
Now, Newton? That's more like it. Nobody reads a large amount of his mathematics unless they're some variety of mathematical historian.