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I am in the process of finishing up writing my first paper, and I have a question on style.

How much should contractions be avoided? Specifically, should "we'll" be avoided?

Having looked online, it appears that a lot of people don't like them, at all. However, with my years and years of experience that comes with $1$yr of PhD (=P) I feel that this may be too broad a rule.

I agree that writing some contractions, for example "this won't be able to..." is likely to be a not a good idea. However, I feel that the case of "we'll" is more subtle. Either one has to write "we shall" everywhere, which seems overly formal and/or old-fashioned, or write "we will". While I agree that language evolves over time, "we will" is very unnatural to say -- specifically the two w-s in close succession; other languages get around this with apostrophes also, for example saying "l'acqua" in Italian, rather than "la acqua". Sometimes "we will" is better, eg if you want to emphasise that you will, or just reply "yes, we will" -- hopefully no-one replies "yes, we'll"!

I feel that a paper should be written so that it reads as fluidly as possible, putting all the focus on the actual maths. As such, using "we'll" sometimes (not necessarily always) seems far preferable.

I'd be interested to know if I'm the only one that feels this way, and to be advised on how to use this! (Being a native (British) English speaker myself, I also can't comment on what it's like to read "we will" as a non-native.)

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    $\begingroup$ I suggest that instead of worrying about this, you worry about avoiding the passive voice: "How much should contractions be avoided? " => "Should I avoid 'we'll' in my mathematical writing?" :) $\endgroup$ – John Hughes Mar 15 '18 at 11:12
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    $\begingroup$ To whoever voted to close, instead of doing this without leaving a comment to suggest improvement, can you explain how I should edit my question so that you feel it is more appropriate for the site? Under the tag article-writing is written this: "Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes". To me, my question appears to fit that perfectly $\endgroup$ – Sam T Mar 15 '18 at 11:18
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    $\begingroup$ @JohnHughes I only added in the specific bit about "we'll" after. I'm not sure passive voice is an issue though: this website is supposed to be a resource for other people, not just for me to have a specific question answered (at least I hope my question can help others!) :) $\endgroup$ – Sam T Mar 15 '18 at 11:19
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    $\begingroup$ (Btw, though sometimes passive voice is silly, it is harmless.) $\endgroup$ – paul garrett Mar 15 '18 at 11:59
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    $\begingroup$ One point. A mathematics publication will (we hope) be read also by those whose English is weak. So writing "we will" and not "we'll" is a small price to pay to increase comprehension for those readers. It is much more important than whether "we will" sounds stilted or formal. $\endgroup$ – GEdgar Mar 15 '18 at 13:44
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Non-native english speaker here, with a bit more experience than you but not that much.

I don't think you can go wrong with being formal when you write mathematics. Phrases like "hence", "thus", "We shall see that..." are kind of common (though "hence" and "shall" are probably near the upper limit).

"We will" doesn't sound strange to me, but again I am not a native speaker.

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