Using "we" in a paper.

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I'm the sole author of a paper and in my introduction I've written:

We are able to talk about... Doing so we manage to capture ... We accomplish this by embedding...

and I'm wondering whether it's correct to talk about myself in the plural like that, similar to the way that mathematicians tend to write when talking about some mathematical fact or proof. If not do I just write things like "I am able to talk about"? Because that just sounds odd.

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As odd as you may feel it is, using first person singular is usually frowned upon, as we, and first person plural is preferred. Additionally, third person, in the form of "The author," can also be used, especially with acknowledgements (The author would like to thank x,y,z for their contributions).

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Yes, this is completely standard. In fact, the first-person singular is almost never used in technical papers. Even in the acknowledgments, it's common to say things like "The author would like to thank..."

You can think of the 'we' here as referring to you and the reader, working together.