David Auburn's Proof plays with the audience, cannily withholding elements essential to the story taking place before our eyes in a back garden, adjacent to the University of Chicago. The first of those elements arrives after a lengthy gentle conversation between a relaxed, reassuring professor of mathematics and his earnest, worried daughter. Similar to an instruction to divide by the square root of -1, it obliges new rules upon us, sending us off into the world of the imaginary.
Auburn does it again at the close of Act I, when Bridget applies an operator that's similar to [*-1], giving our results a smart shake that turns our received knowledge inside out. And since in good story telling tradition surprises come in 3's, he situates the opening of the second act not in n but rather in [n - x] where x = 4 and the units are years.
Leaving math play aside for a moment, one intriguing aspect of Auburn's story about the frontiers of mathematics and the far reaches of human rationality is how little of mathematics appears in it. Of course, your ordinary audience would probably sit glassy eyed at any serious intent to explain a major postulate or proof. We who are largely innumerate take the existence of higher mathematics largely on faith, and we're perfectly satisfied when Auburn withholds the mumbo jumbo of technical terms for the the final seconds of the piece when the stage lights are going down. Catherine, granted credence by her aspiring suitor the graduate student in math, is about to take his adoring attention into those mythical realms where we can't follow.
Proof only hints at mathematical proofs, exercises in a closed and shining world where everything fits incontrovertibly. More importantly, it offers us the search for proof in a more judicial sense -- the messy accumulation of facts, testimony and human interactions intended to establish in our fallible mind , beyond a reasonable doubt, a version of reality.