Which of the following expressions makes more sense when talking about Dr.X's paper ?
(1) "Dr. X wrote a paper in which he showed Y."
(2) "Dr. X wrote a paper where he showed Y."
(3) "Dr. X wrote a paper showing X."
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11 & 3 are fine. There's little to choose between them. I'd avoid 2. Where doesn't fit comfortably here. – Ronald Sole Nov 7 '20 at 18:10
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Dr. X wrote a paper in which he showed Y.
I think this is the most correct of the three.
Dr. X wrote a paper where he showed Y.
I think this is perfectly acceptable but I also think it makes more sense to say that something is demonstrated in a document rather than using "where" which has a more spatial connotation.
Dr. X wrote a paper showing X.
I think most grammarians would opt to stick with the past tense of show in line with the past tense of write but there is no hard and fast rule here. This version is more conversational than the other two.
My version may look something like this depending on what the paper actually accomplished:
Dr.X authored a paper that proved Y.
Dr.X authored a paper that suggested Y.
You get the idea. When you can, use descriptive words. Did he more-informally write a paper or did he author one? Did the paper show something or did it prove something? Beautiful language is one where every word counts.
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I don't find the verb author to be in the same universe as "beautiful language", but that's personal preference. And you seem to be assuming that showing is "present" as opposed to "past": it isn't. It hasn't got a tense: it's contemperaneous with the matrix. – Colin Fine Nov 7 '20 at 18:12
