Using "we" in mathematical reports Recently, I have submitted an early draft of a report summarising the results of a year-long project at my university, to my advisor for review. We have met up for a review of the paper, and he pointed out my frequent use of the word "we" in the paper. He considered it a mistake and asked me to change everything to a third-person view.

Personally, I found this incredibly strange. I am in the field of mathematics, and based on other papers and publications in math, it is very common and even considered "good" language to use the word "we" in writing, especially in proofs and discussions of results. For example, instead of


  This proof demonstrates Theorem 3 to be true


it is considered desirable to instead write


  We have thus proven Theorem 3.


The reasons cited for this preference, I have seen, is due to both convention and to avoid dodgy writing (third-person wording may suggest that the authors did something, but it could have been taken from somewhere else).

I have seen different questions on this site pertaining to this issue. This question, for example, has answers which suggest to take reference to the style guide provided by one's university, which unfortunately mine does not have. The accepted answer deals with economics, so I am unsure it applies in mathematics. This question suggests it is good to use "we" in mathematical and scientific writing. A quick search on Google, however, apparently suggests it is always undesirable to use first or second person pronouns in academic writing (see this site).

Thus, I am asking this question for my specific scenario for clarification. Should I follow my advisor's advice, or should I discuss with him further? Again, I find his advice rather odd and I definitely prefer to be able to use the word "we" as I please when appropriate.
If you were writing for a journal, you would want to check the journal's style guide. If it doesn't cover that issue, then the next step would be to check previous publications and see what the norm is.

For an internal report with no applicable style guide, one should write for the intended reader/s. If your advisor is going to be the main reader for this document, then write it in the style that he requests.

To me, this change seems unnecessary, but it may help to consider this story from the development of the computer game Battlechess:


  The producers of the game were known to demand changes to the game, presumably to make their mark on the finished product. To this end, one animator added a small duck around the queen piece, but made sure that the sprite would be easily removable. Come review, the producers, predictably, okayed everything but asked for the duck to be removed.


In my experience, this is a very broad tendency among managers/advisors, and now that I'm a manager myself I understand the temptation to micro-manage. Even if a document is quite good enough as-is, if we don't suggest changes we don't feel like we're doing our job. 

It may be that your use of "we"s is the sacrificial "duck" shielding you from more annoying change requests.