Stylizing Rigor: or, Why Mathematicians Write So Well

We know, by now, how to talk about most sciences through the lens of rhetorical analysis. However, certain disciplines, such as mathematics, seem to have escaped the reach of those pesky scholars of rhetoric. A possible reason for this is that when we are told that a certain piece of writing is "rhetorical" we often imagine this to mean that it employs deliberate strategies to generate belief or trust in the reader: thus rhetoric becomes a matter of credibility. And it does seem hard to talk about mathematics in just these terms. But if we expand the field of inquiry, and also ask the question of a text's significance, its means of generating credit, then we also have the problems of relevance and value to work with: Who should care what scientists or mathematicians have to say, and why? In the case of mathematics, we cannot begin to speak of credibility without also taking into account creditability.

Before bothering about whether a mathematician is telling the truth, an audience needs to judge whether it is a truth worth listening to, and indeed, what worth is in the telling at all. Most mathematicians work with ideas that have no point of reference, not even via potential technological application, in most people's lives. And the claims that mathematicians make are usually not intelligible to anyone but the expert in a particular subfield of mathematics (excluding rare cases such as Fermat's Last Theorem). Nevertheless, as producers of cultural products the ultimate legitimacy of which is at the mercy of society at large, mathematical communities would at some point need to make a case for their own relevance, and take up a position within their social milieu. Yet it is hard to find instances of a serious dialogue occurring between mathematicians and the public. The nearest candidates seem to be accounts given by workers in the field which appeal to the aesthetics of mathematics and develop analogies with various high arts; but in spite of good intentions, such accounts may only further mystify what they purport to explain.

These strange relations with the public may be illuminated by exploring the relations of mathematics with other sciences. Thomas Gieryn has discussed ways in which scientists have established bounds for their disciplines by cultivating dichotomies between themselves and nonscientific disciplines (religion or engineering, for example).¹ In contrast to this, mathematics sets its bounds almost entirely through antitheses with the natural sciences. Consequently, its boundary with other nonscientific communities tends to become obscured, with little need of border-guards and nearly no consequential assailants at the gate. Of the disciplinary boundaries with other sciences, it is particularly at that between mathematics and physics that the most intensely coordinated efforts go into establishing and protecting notions of what is to be considered valuable as mathematics.

I will argue that these boundary phenomena (some actively contested, and others all but dormant) are bound up with specialized writing practices in mathematics. Most of the work in science studies that has linked rhetorical strategies to the development of scientific communities has focused on some area related to experimental science (see, for instance, the work of Charles Bazerman and some of the work of Steven Shapin, among many others), and thus the idiosyncratic position of mathematics has gone somewhat neglected. This is a significant oversight since, as we will see, mathematicians engage in a strategic reversal of some of the principal doctrines of writing that we tend to associate with the natural sciences. Indeed, notions of how mathematical texts should be written and read generate distinction (difference and eminence) by opposing mathematics to the less dignified scenes of writing that are imagined to characterize the natural sciences.²

In section I, by studying the guidelines and recommendations set out in various writing handbooks published by the American Mathematical Society, I will suggest ways in which the canons of mathematical writing practices have been structured via opposition to...