Deus ex machina and the aesthetics of proof

C Unexpectedness and inevitability, two of the aesthetic qualities G.H. Hardy identified as being properties of beautiful proofs [Har, §], together seem paradoxical: how can something be seen as both unexpected and inevitable? Two possibilities are that the inevitability only becomes apparent in hindsight, or that the strategy of the proof is unexpected but, once chosen, proceeds inevitably. In this essay, I suggest a different solution: I argue that the literary concept of deus ex machina can be used to clarify the notion of inevitability in proof and reconcile it with unexpectedness. Deus ex machina (literally, ‘god from the machine’, henceforth abbreviated to deus) refers to a type of plot device used to resolve a seemingly intractable situation. The term is derived from ancient Greek drama, where such a resolution might be effected by a god intervening, with the actor playing the god being lowered onto the stage by a crane (the ‘machine’). It has come to mean any event in a story that resolves a situation but which does not fit with the internal framework of the plot [LE]. Aristotle is the earliest extant author to complain of the unsatisfactory nature of such a resolution [Poetics, a–b], and this disdain has continued to the present day. Aristotle gives the example of how Medea, at the end of Euripides’s play of the same name, is rescued from Jason’s vengeance by being carried off toAthens in the chariot of the godHelios [Medea, l.]; until this point, the play is free from divine intervention.