Math Textbook Reflections

 As a student, I've found myself intimately engaging with very few math textbooks. That being said, “Fundamentals of Complex Analysis – with Applications to Engineering and Science 3e” by E.B. Saff & A.D. Snider holds a special place in my heart. It was/is clear to me that it was written for students. Often ideas are presented as stories. The authors frequently use “we” and “us” to indicate that they are taking you, the student, on a journey. Provided you engage with this text as intended (reading without skipping), one finds that the dissemination of knowledge is paced very deliberately. It gives one time to digest and question new ideas before throwing the reader to the (mathematical) sharks. In this way, I suspect that those familiar with the ideas presented would find very little value – the pacing is intended for a new learner.

In the relevant article, I was interested in comments relating to first person pronouns. It reminds me of Drakulic’s ‘Café Europa’, in which she discusses her tendency to use the first personal plural ‘we’, as well as her hatred for this tendency.  For Drakulic, the use of ‘we’ is associated with anonymity – it is the movement of a massive, automatic, submissive puppet. Conversely, ‘I’ is associated with the development of individuality, responsibility, democracy, and initiative. Despite this, Drakulic often speaks with the first personal plural because she acknowledges a common denominator between members of all formerly communist states and herself.

Drakulic shows us that when the use of ‘we’ is natural when we are speaking on behalf of a community. Textbooks which use ‘we’ and ‘us’ speak on behalf of the mathematic community – a community that both the author and the reader is a part of. With that in mind, the use of ‘we’ also suggests a submissiveness on the part of the author – by using plural pronouns, one doesn’t get the sense that the author is speaking about their own ideas, but rather is escorting the reader through some well defined (mathematical) reality. Perhaps ‘submissiveness’ is too harsh… Regardless, there is enormous value in texts infused with the first-person singular. Such text would reflect on the author’s personal experience with the material, un-abstracting concepts from the distilled realm of elites. Paul Lockhart’s ‘Measurement’ is a fine example of this.