[Machow]

For what it's worth, in Psychology (by APA standards) 1st person voice is discouraged, but so is passive voice. In the passages you use, removing 1st person (almost) requires using passive voice, but I would say removing 1st person voice is what discourages a very informal, prosey style, while the frequent use of passive voice often feels indirect.

[graycat]

> 1st person voice is discouraged

"Here we make use of measurable selection."

So, use of the first person, plural is quite widely accepted in nearly all of current and recent mathematics.

I wrote my Ph.D. dissertation this way, and one professor said "When you say 'we' maybe I don't agree?" and thankfully a fellow student spoke right up and defended me; she explained that using "we" was standard in mathematics.

Once I was trying to socialize with a high school English teacher and sent her a draft of a paper I was about to publish in some applied mathematics and asked her to give the paper a critical reading. Soon she asked me if using "we" was standard in mathematics, and I had to say yes. She gave me no more feedback! Gee, that's much better than what I got from English teachers in high school and college!

In the end, I first learned to write in college and by writing proofs in pure mathematics; the reason I was able to soak up the lessons was that such writing, as English, is so darned simple. Later I branched out from such simplistic writing.

Later I was trying to socialize with a woman who was a secretary in a university. She confessed that, in her experience typing, etc., the really clear writing was from the professors of mathematics and the physical sciences. Maybe she was just trying to butter me up!

[seanmcdirmid]

I use "we" all the time...but I try to make it mean "me and the reader", i.e. "we then look at ....". In that sense, a paper should be a conversation between you and the reader even though the reader is passive in the interaction.

[pimlottc]

I'm struggling to figure out how you would write lab instructions in neither 1st person or passive voice. Would you just credit all actions to an anonymous experimenter, described in third person?

[Machow]

That's fair. For psychology methods it's easier to avoid both, at times, since you can write "participants viewed...", etc.. For other types of methods, especially where the object becomes implicitly understood, or would be redundant to state, I can see where passive voice might be useful. For instructions, you can just leave off the implicit "you should", EG "put X in Y". The tradeoff between passive and first person is important, and which is appropriate likely depends on the circumstance. They're both discouraged, but not banned, I'd imagine because poor writing often uses one or the other too often.