The discussion centers on the use of "we" versus "the result is" in writing about analytical geometry and linear algebra. Participants debate the implications of using "we," which can create ambiguity about who is included, while "the result is" offers a more neutral tone. Some argue that using "we" can enhance engagement by including the reader, similar to how it is used in lectures. However, others prefer avoiding first-person language in scholarly writing to maintain objectivity. The conversation highlights a shift in academic writing preferences toward first-person narratives and active voice over the past few decades, although opinions on this vary among authors and publication venues. The use of "we" is common in mathematical texts, but its appropriateness in web writing is questioned, as it may not clearly convey the intended inclusivity to readers. Overall, the discussion emphasizes the importance of clarity and engagement in academic writing while navigating personal style preferences.