The paper you posted is a good example. The conclusion is:

    sudoku = map (map head) . search . prune . choice 

Note how the "code" never mentions the data to which it is applied, namely the Board object. This is why I can't agree with the GP's argument that FP is closer to "code" than anything else -- I think it's as far from "code" as you can get. There are no "instructions" here, just an equation representing something complex ("the solution to sudoku"), in terms of slightly simpler parts. The simpler parts are, earlier in the paper, the complex parts; and are of course described there by simpler parts.

And, this is not just something that's useful for esoteric mathematics papers; my "enterprise" code in Haskell looks very similar.

"Functional Programming is more like mathematics." I would completely agree. In fact, I would add to that and say FP is mathematics because its "Functionally" based and was originally created for easy inductive proofs.

However, from a readability standpoint, english is better than mathematics, and readability counts for quite a bit if you aren't planning on throwing away your code.

"However, from a readability standpoint, english is better than mathematics"

That depends on what you are reading. Try reading differential calculus in English, without using notation.

Not to take anything away from your point (and I think it is a good one), but there are all kinds of code. Functional Programs can be astonishingly elegant.