The problem you're running into is that people who have some "mathematical maturity" don't get bogged down in notation, so it's difficult for them to see the distinction you're trying to draw between e.g. `{ x∈S | x.id = 1}` and `select x from S where x.id = 1`[0]. You say "a SQL query is a SQL query" and they just think "yes, which is also obviously a mathematical expression".

Computer programs are proofs[1]. This is intuitively and also formally true. You would agree writing proofs is doing math, yeah? Then obviously writing a computer program is also doing math.

Like I have a degree in math and have been a software engineer for over a decade. I do not know what distinction people are trying to get at. It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing". Or saying that writing C is programming but writing in a functional language like Scala or Haskell (or Lean) is not.

[0] Modulo details like NULLs and multi-set semantics, but surely that's not the distinction?

[1] Up to isomorphism