This reflection is due to a comment offered by an audience member after I presented a short paper on this work at the Bridges Conference for Mathematics and the Arts in Baltimore, August 2015.
Alongside the step-by-step addition of more information offered by the laying out of symbolic expressions in a mathematical presentation, and the recipe-style instructions for how to direct these expressions to arrive at a proof, run three distinct narratives.
One is the narrative of the history of the question and the pieces of mathematics used in the proof, evoked by the naming of theorems (“this is true by Khan-Markovic”). I have written a little about this historical referencing here, particularly because often an idea is named not after the person who first came up with it, but somebody a couple of generations down the line. This naming therefore evokes a cast of ancestors to the mathematics, historical faces that suggest greatness, but whose selection is governed by more complex social factors than are immediately obvious.
The second narrative is a reconstructed account of the attempt to prove the mathematics, enacted by the presenting mathematician to aid the audience in their attempts to create the mathematical meaning in their minds. The work is already proved and published, but presentations are littered with the language of endeavour: we’ll try taking this instance, we’ll apply this idea and see where that takes us. This suggests a fictionalisation of the process of working through the mathematics.
The third is of course the true story of how the proof was found, which is very seldom told. The popular blog overly honest methods highlights the schism between the scientific method reported in journals and the messy realities of research. Latour and Woolgar also observed ways in which scientists’ accounts of the emergence of a discovery differ from the events they observed in their study of Laboratory Life. Ideas might be the result of some mistake that was then rectified or borne of a chance conversation, the key insight of the proof might have emerged early or late, but none of these details are included in the presentation of a proof, or indeed recounted anywhere else.