Say in a face-to-face conversation, if a researcher says "You must be reviewer #X of my paper!", which is true, how should one respond?
(I doubt this would be field-dependent, but I'm mainly interested in the norm of the mathematical community)
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My answer would probably what I really believe to be true:
Nothing good can generally come by thinking too hard who a specific reviewer might have been.
That's true, and it's also a deflection. Anyone with social skills will drop the topic. If they insist, I'd just repeat the statement until the point sinks in.
Related anecdote (not an answer).
Years ago I submitted a paper to journal X. Nearly a year passed with no referee report. I bothered the editor periodically, and they told me they prompted the reviewer.
At a conference I attended I struck up a casual mathematical conversation with someone I knew only from his work. He was very interested in what I was doing, so we spent a long evening together where I explained the results in my paper.
Very shortly thereafter the paper was accepted. The inference is obvious. Neither of us ever talked about this matter, but we went on to do some joint work.
Actually, since the question is a bit improper, you can answer any way that you like. But answering such a question with
Why would you even think that I was?
seems to be a good start, answering a question with another question.
The only really bad answer would be one that results in a fight, short or long term.
That isn't really a proper question.
Even a lie in response to an invalid question is only a minor infraction of social norms (IMO). Especially so if it avoids a fight.
"Why would you even ask such a thing?"
Tone of voice should convey that, no, you don't actually want an answer, you want them to recognize the impropriety of the question and move along smartly.
"I can neither confirm nor deny."
This is from the defense community, and is a standard way to tell, e.g., vendors and sales representatives (among many others) to back off and stop asking unanswerable questions, because it's really rude.
As a response different from the norm: I have had reviewers of my papers not only tell me that they reviewed my papers (confirming my suspicions, but unsolicited!), but also collaborate with me or recommend other collaborators.
I think this would generalize to smaller communities, where maybe only a dozen people in the world will review studies on a particular technique or subject. In my case, my mentor pointed out that the reviews in question raised valid criticisms, and responding to them strengthened the final paper.
If the review itself is professional and helpful, then knowing the reviewer wouldn't do that much harm, especially in a small community if the risk of no review or an unexpert review is far greater than the risk of an unconsciously biased review.
Obviously this person is just really happy to have 'found' you!
Writing math paper is a strange experience. The person has probably spent a long time in a very intensive relationship with mathematical objects that no-one else around them can see or hear or has even heard of. Writing things down in theory makes it possible that other people will learn about this world where they spent so much of their time, sorrow and joy over the last few months, but hey, let's not kid ourselves, almost nobody reads math papers for fun and those who do have a pile of 100s of papers they hope to get to someday.
So after spending all this blood, sweat and tears there is only a small handful of people that even know the characters and places that made up such a large part of your life, and as they are anonymous and scattered around the globe there is no hope of ever meeting them.
Now running into one, by chance, in real life, is a magical experience!
I think the cold reactions advertised in the other answers are undeserved and do no-one a favor. The best action is to reveal yourself and have a nice chat about the content of the paper.
Simply by having carefully read the paper and being a person of flesh and blood you can make this researcher's day in a way no one else can. Who would pass up such an opportunity?