This is related to an earlier question: "parentheses" vs "parenthesis" but is about etymology of the related (and apparently informal, per wikitionary ) word "paren" and more in line with the rules of being "on topic".
As some answers and comments to the linked question point out, the "official" English words are so similar it is confusing. For one, "parenthesis" can mean a singular "(" or ")" or it could be the contents between "(" and ")". So, its meaning changes depending on context but both meanings are used in very similar contexts and could easily be confused. Additionally, one rarely uses the singular form in the English language. Furthermore, they are so close in spelling and pronunciation that they are easy to confuse visually (without reading slowly) and audibly (without an awkward additional stress on the final syllable). Therefore, these words are problematic in the language.
In the tech industry and similar circles, the need for a singular version is more common as the single characters "(" or ")" may appear on a line in computer code, on a keyboard or keypad, or for use in emojis. I believe (though I do not have a source) that this word is used not just to shorten "parenthesis", but also to eliminate the confusion mentioned in the linked post. When you say "paren" you cannot mispronounce or use it in a way to be confused with the plural "parentheses". Whether that hypothesis is true or not, in my field of work, it works to use it and it is used commonly. In fact, personally I have used "paren" quite often lately and of course I use "parentheses", but I don't believe I've ever used the word "parenthesis" (when I was younger I often used "parentheses" improperly as both singular and plural). As an engineer, I'm probably overexposed to the usage of this word, so I don't really know how common it is or not. It seems I've only been using it myself in the last few years (perhaps it was less common 7 years ago when the linked question was asked).
In addition to defining it as a synonym of "parenthesis", Merriam-Webster does cite a usage of a pluralized form "parens" from 1985 in its definition. However, every time I've noticed, people around me use the long form "parentheses" for the plural, making it an interesting singular/plural pair (paren/parentheses) that I don't believe is similar to any others in the language. This citation does show the word was used at least as far back as 1985 and that its use was technology related, but I haven't found an official first usage anywhere.
So, my questions are:
When did "paren" first start being used as a shortened form of parenthesis?
Can anyone confirm or disprove my hypothesis with one or more sources that "paren" has been adopted by people in the tech industry to minimize the confusion of using "parenthesis"?
How common or uncommon is the usage of "paren" outside of the tech industry?
Side note: I'm born and raised in the United States and I know it's not technically proper grammar here, but I prefer the British standard of punctuation that is not part of a quote to be outside of the quotation marks, so those grammatical "errors" in my discussion above are on purpose. To me, having them inside the quotations marks just does not make sense if they are not part of the quoted word or phrase regardless of what official rules say... but that's another discussion.