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.)
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.