Mathematics and computer science having little to do with linguistics seems to be more often the position of people with an interest in the former two than a generally shared perspective. It's true that programming languages are formally mathematical, but they're still languages with grammars and parsing and even room for implication and ambiguity and authorial expression now and then; and math or no, learners often find framing, for example, object orientation in terms of nouns and verbs more intuitive than staring at proofs.
Manufactured languages, software architectures, and specialized interfaces are much more limited in scope than natural languages, texts, and grammars. But there are still rules they conform to and tendencies they exhibit, so it's rather a waste of time to ignore the vocabulary and theoretical toolkit already developed for us by linguists and semioticians. And of course, treating natural languages themselves in mathematical terms is a topic of no small interest on either side of what dividing line exists.
I totally agree with you. I'm a failed mathematician and an unsuccessful linguist :) But I think the fair reply to the OP is that there are no proofs that linguistics as a scientific field has influenced computer languages anywhere close to the way mathematics have.
I'm re-reading all the replies and yes, there are plenty of proofs, as was referenced in the exchange. I was just stuck in my vision/experience of linguistics.
My understanding of the OP's question was more in the field of programming language design (as Ben seemed to hint) where an influence of linguistic research would have contributed to produce languages closer, in expressiveness and structure, to native languages. So I was considering only a very narrow aspect of both computing and linguistic research.
Thank you Dian and Yucer for the really interesting comments.
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