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I am interested in answers to this question particularly as it pertains to mathematics.

To be more specific, I am interested in using the passive voice in mathematical proofs as I feel that this reinforces the objectiveness and universality of the proof as opposed to the specific instance of the proof or my own self. However, it is my understanding that the first person plural present tense active voice is the norm in mathematics. I want to use this uncommon style in papers and other proofs for these reasons. However, I am concerned this may tarnish my reputation. Would it be looked upon negatively to intentionally employ a writing style uncommon in my field to express what I see as key values in the field?

  • I realize that this is not well phrased. However, I lack ideas as to how to improve it and would appreciate an answer. I am also open to suggestions and assistance in improving this question. – user29175 Mar 11 '17 at 22:21
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    Providing an example would be nice. I'd also recommend providing a reason as to why you feel this unconventional writing style is necessary. Basically: fill in the background of what you want to do and why you want to do it. – tonysdg Mar 11 '17 at 22:24
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    This is so so vague. What is a "writing style uncommon to mathematics"? (Why not just tell us what writing style you plan to use?) What do you mean by "express key values in the field"? (Why not just tell us what values you plan on expressing?) Negatively in what context? (Why not tell us where you would be writing such a thing? Is it for a thesis? A journal article? A blog?) etc. – Antonio Vargas Mar 11 '17 at 22:26
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    Passive voice is so common that I disagree that active voice is "the norm". Active voice is advised by some style guides, yes, but there is absolutely no way choosing passive over active would be perceived as "unbecoming". – Antonio Vargas Mar 11 '17 at 22:34
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    There's something missing from the sentence that begins with "however." // Could you please give us a short paragraph from your draft so we can see what you're getting at? – aparente001 Mar 12 '17 at 3:43
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You are not very specific: on the one hand, there is more than one kind of mathematical writing; on the other hand, you write "I am concerned this may tarnish my reputation" and that depends (a little bit, at least) on who you are.

I will assume that you are a junior mathematical writer, i.e., that you have not yet published many (or any) mathematical papers. (If you have already written a few dozen papers, you have not only a lot of experience but have gotten a lot of feedback, so you know what kinds of writing variations referees, editors and other careful readers will pay attention to.)

Let me begin with some (unfortunately rather conservative, but still inherently sound) advice for the journeyman writer in any academic field:

Don't try to be innovative or different in your writing style in your first papers or first years of writing papers. First learn how to write acceptably -- or better, well -- according to the most standard norms of your discipline.

It takes a while to master the standard conventions of academic writing. When I look back at some of my earliest papers, I see some weird stuff. In a few cases I was trying to be innovative, but most of the time I just didn't know what the standard convention was. About 50 papers in, I am still learning new things about the standard mathematical style.

What's so great about standard mathematical style? Nothing inherent. But as a culture, we're used to it.

The cardinal goals of mathematical writing are precision and clarity. After that, the next goal is unobtrusiveness: good mathematical writing does not call attention to itself, because attention that is diverted to the writing is diverted away from the mathematical ideas and reasoning.

Again, what is unobtrusive depends on the culture. For instance, there are some mathematical turns of phrase that would be pretty weird in ordinary writing but are not weird in mathematical writing because they have been done so many times before. Examples include: "in the sequel," "by abuse of notation," "a trivial case"...And of course the best example is the use of "we" in mathematical writing. It looks pretty weird the first N times you see it...and then it doesn't. It is an entirely standard convention of mathematical writing, as can be seen by its approved use in virtually every mathematical style guide but even more strongly by its almost universal use in published papers. You don't have to use "we" in mathematical writing -- e.g. this style guide contains some tips from Paul Halmos on avoiding it -- but I can think of no good reason to avoid it.

Every mathematical style guide known to me denigrates the passive voice in mathematical writing in the majority of instances. So for a journeyman mathematical writer to insist on using the passive voice would be a violation of both of the above pieces of advice: on the one hand you are not learning to write in the standard way, and on the other hand you are writing in a nonstandard way that a lot of your readers are going to notice, get mildly distracted by, and therefore in some cases get moderately annoyed at you for writing in this way. Why do you want to risk this? You say:

"I am interested in using the passive voice in mathematical proofs as I feel that this reinforces the objectiveness and universality of the proof as opposed to the specific instance of the proof or my own self."

Honestly, I am very unsure what you mean by that. In case you are suggesting that there is some logical or ontological difference between

We will show first that A implies B and then that B does not imply A

and

It will be shown that A implies B and then that B does not imply A

I can assure you that there is not. More to the point, readers of math papers are not going to be critiquing the proofs for "objectiveness": I don't even know what it would mean for an otherwise satisfactory mathematical argument to lack objectiveness.

Moreover, what are you actually trying to accomplish by using the passive voice in your math papers? It can't be to make your work easier and more pleasant to read...as you seem to understand already. You write

"Would it be looked upon negatively to intentionally employ a writing style uncommon in my field to express what I see as key values in the field?"

What "key value" is expressed by using the passive voice? I don't think there is one. But if people get wind of the idea that you feel like you, as a junior person, are in personal possession of a clearer understanding of the "key values in the field"...Well, since you asked for feedback, my honest appraisal is that you sound a little nutty and a lot inexperienced. So it is a bit of a negative, yes. Of course, all mathematicians start out a lot inexperienced, and many, many of us are a little nutty, so your eccentric-sounding ideas about writing and mathematical values will not be a major sticking point in your career.

The largest issue I see, honestly, is the impediment to learning good writing that you've placed on yourself. Without meaning to be harsh: parts of your question remain obscure to me after repeated readings. The comments show that other readers feel the same way. This is a real example of your writing not being properly understood by others, perhaps to the point of your overall message getting lost. That's the risk you incur by not placing a premium on clarity. It's a big one.

  • Actually, you seem to have understood my question well, thank you for the advice and feedback. – user29175 Mar 12 '17 at 12:40
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Some style guides (e.g. Knuth et. al. [PDF link]) advocate using the active voice over the passive voice. One reason for this is that some readers find the passive voice boring.

There are, however, many examples of mathematical writing using the passive voice, both in books and papers. If the goal is that mathematical writing should be engaging and lively then the use of the passive voice could be seen as a bad habit among some mathematicians.

That said, there is absolutely no way choosing passive over active would be perceived as "unbecoming". You may bore your readers (so much so that they don't even care to read what you've written), but that's about the worst you could expect.

  • Thanks for this, if I haven't accepted an answer in a few days, you may want to remind me. – user29175 Mar 11 '17 at 22:47
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    @Benjamin I feel that asking Antonio to remind you of accepting his answer is sort of impolite. If you don't want to accept his answer right away, you may set yourself a reminder. – lighthouse keeper Mar 12 '17 at 12:30
  • @lighthousekeeper I am not asking him to remind me, I am saying that if I have not, I may have forgotten. However, I also have a timer for myself. – user29175 Mar 12 '17 at 12:35

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