I'm not the GP, but I'm sorry you felt gatekeeped. I don't think GP conveyed "real mathematicians should do FP", but rather something else, so I'll try my best to share what I understood from that comment. Hope this makes you feel better.

Even though the notation changed over the years, the paradigm of "numbers as immutable entities and pure functions" has been the dominant way that math is presented, compared to something like "encapsulated objects that interact with each other via sending messages".

I don't think this has to be this way, and I do think that "real math" can also be laid out assuming principles of OOP. However, I do suspect it's the way it is because the laws of nature are unchanging, in contrast to the logic of a business application.

Because Julia is a tool with the target audience of mathematicians and scientists, I think it's a sensible decision to embrace the usual way of thinking, as opposed to presenting a relatively different way of thinking which steepens the learning curve. Not because data and functions are fundamentally better than OOP, but because it's more pragmatic for the target audience.

I understood the other poster correctly. This view of mathematics is as limiting and ignorant as the other poster’s.

The entire field of theoretical computer science, to which functional programming and type theory is closely tied, is a branch of mathematics. The Church-Turing thesis which gives both to our field equates the two at a very fundamental level. Questions about type theory, programming language design, and programmer ergonomics are fundamentally about math and applied math.

Maybe you and the other poster have in mind specific fields of math, but then you need to make claims for why those fields are sufficiently different as to be exempt from applicability of any of the advances in notation observed in other fields.

Your implicit assumption that you can divide computer science into a different bucket from “real math” is incorrect, and gatekeeping.

As I said though, I don’t think this is a profitable debate to have here on HN.

Okay, I see what you mean.

> Maybe you and the other poster have in mind specific fields of math,

Yes, because this is about Julia, I assumed we are talking about the specific fields of math that happen to be commonly used in mathematical and scientific computing, such as the ones learned in university math and science courses.

> Your implicit assumption that you can divide computer science into a different bucket from “real math” is incorrect, and gatekeeping.

It is regretful that we had a miscommunication. I agree with you that computer science belongs into the same bucket as "real math". The thing is, in the context of Julia it is not easy to read "math" as "math, but not only the domains that Julia is concerned in, but really all fields of math, including theoretical computer science". At least thanks to your comment, I see what you mean more clearly, and I think it'll help some other potential readers as well.

> but then you need to make claims for why those fields are sufficiently different as to be exempt from applicability of any of the advances in notation observed in other fields.

I'm curious to know specifically about the specific advances of notation observed in other fields. By this you mean dot notation for method application? I'm unsure if `a.method(b).anotherMethod(c)` is more advanced than `a |> method(b) |> anotherMethod(c)` (Edit: or `(anotherMethod(c) . method(b))(a)`) notation-wise.

I'd like to add another point worth mentioning. When I read the other poster's post, I was thinking about the semantics of OOP, specifically encapsulated objects and messages. I may have misinterpreted the other poster, but I hope it at least makes my other messages a bit clearer. (I think it's a little unwieldy to use Matrices that encapsulate its state for Linear Algebra, for example.)