Speaking as an academic PL researcher: you are right that this math-centered view is common in the PL research community, but that doesn't make the opposing view "wrong". There is also plenty of work in the intersection of PL and HCI. Both perspectives are crucial, and neither field is intrinsically superior to the other, despite what some individual researchers feel.
A human view of programming languages - Amy J. Ko
In computer science, we usually take a technical view of programming languages, defining them as precise, formal ways of specifying a computer behavior. This view shapes much of the research and development that we do on programming languages, determining the questions we ask about them, the improvements we make to them, and how we teach people to use them. But to many people (even software engineers) programming languages are not purely technical things, but socio-technical things. In this talk, I discuss several alternative views of programming languages, and how these views can reshape how we design, evolve, and use programming languages in research and practice.
The upshot is while the "PL as math" and "PL as tool" views have been well researched, if you're a researcher getting started in this area there is plenty of fertile ground out there. We might just have this view that "PL is math" because we've done the most work there, but there are many more applications of programming languages we have not thoroughly explored enough to say they are not just as important.
Yes, “wrong” was a bit of a strong word, but do note that I intentionally framed it as an opinion and not as, like, objectively wrong.
UI is still important, but I do not think it really defines a language.
Let’s say I created a new Haskell compiler, and it had the best error messages in the world, a hiccup-free LSP experience, maybe an alternative syntax format that’s more familiar to mainstream devs. But it still has all the same semantics. Is that still Haskell? Why or why not?
Now let’s say I took whatever has the best tooling currently, idk what it would be, maybe TypeScript, but gave it say non-strict semantics. Is that still typescript?
If you consider the programming experience/UI to be the language along with the tools that support that language, then you don't need to concern yourself if using Haskell in vim is the same thing as using Haskell in an IDE that supports it really well, they aren't the same thing.
If you take it to an extreme, like with Smalltalk, you wind up with languages whose environment is considered essential, they are basically part of the language at that point.
