Your friend asked a good question. I do not think that "who" or "whom" can ever be used properly to refer to anything non-human.
The meaning of the example sentence is unclear and certainly not idiomatic. The word "number" has slightly different meanings. In the absence of context, which of those meanings is intended must be clarified with additional verbiage. So one possible meaning is:
Would you tell me the phone number of the person who wrote this paper?
It makes sense to say that a person has a phone number, but, except for acute psychiatric cases, a person cannot be plural and thus cannot have an unknown number in the "counting" sense. With the addition of "phone," the sentence makes sense, but, to be grammatical, "who" is definitely the correct pronoun rather than "whom."
It is the role of the pronoun in the subordinate clause that determines the distinction between “who” and “whom.”
Would you tell me the name of the person who hit Jane
Would you tell me the name of the person whom Jane hit.
The two sentences above have entirely different meanings: in one, Jane was the person struck, requiring "whom," and in the other, Jane was the person doing the striking, requiring "who." It must be admitted, however, that except in fairly formal writing and in the speech of very careful speakers, this distinction in usage between "who" and "whom" is often ignored.
Possibly the intended meaning of the given sentence in the original post is
Would you tell me the number of people who wrote this paper?
If that was the intended meaning, "who" is the grammatically correct pronoun because it is again acting as the subject of the subordinate clause. But notice that " number" has now been clarified with "of people." People can be plural, and so the "counting" sense of number may be relevant.
I must agree with Kevin that, if this second meaning was intended, the addition "of people" still makes this sentence unidiomatic regardless of the choice between "who" and "whom." Kevin is correct that an idiomatic version, which does not involve the distinction between "who" and "whom," is
How many people wrote this paper?