I have very particular ideas about proof. I believe that proofs should be beautiful and, to the extend that this is possible, concise. A beautiful proof should be as slender as one of Shelly's odes, and , like an ode, it should imply vastness. I tried to impress this upon Ramanujan. "A good proof," I told him, "must combines unexpectedness with inevitability and economy." There is no better example than Euclid's proof that there are infinite prime numbers - a proof I am going to walk you through now, just as I walked him through it so many years ago, not because you don't know it (I should hardly wish to insult you by implying such ignorance) but because I want to call attention to aspects of the proof of which your professors, in teaching it, may not have taken note.
In David Leavitt's The Indian Clerk the narrator's voice is that of a mathematics professor delivering an address at Harvard in 1936. The mathematician is G. H. Hardy, an actual historical figure, who Leavitt imagines remembering the story of bringing the self-taught Indian mathematical genius Ramanujan to Cambridge in 1914. This casts the reader in the role of a mathematics student, an interested insider. Hardy is a man who pretty much lives in the realm of abstract thought, and Leavitt is good at integrating his ideas with the events of the story. When he touches on the math, he makes us feel like we're hearing about math while really being very kind to the inumerate.
One thing I am enjoying in this story is that, though Hardy receives plenty of criticism for sheltering himself in abstract thought in lieu of involving himself in social life, in a life of bodily desire, in the world which goes to war in the course of this book one bright side of his obliviousness is how unprejudiced he seems to be. In a sea of white skin when Britain was still the Empire and dark skinned peoples a source of fascination at best and prejudice more usually, this mathematician loved this man for his mind, sought to develop his talents, ate dinner with him (at least as the story is told in this book). His does display some ignorance about his religious beliefs, his diet, and dress - but his interest in him relates to his ability. I think he would have taken the same liberty with a bright young coal miner in trying to take him from his life and develop his talents if he had discovered in him the same potential to solve the unsolved proofs of the day.
One aspect of the story that does not work for me, however, is Leavitt's having Hardy see and speak to the Ghost of his lover. It provides us a window on Hardy's less rational private self and Leavitt makes much of the rational, atheist Hardy seeing a ghost - he does develop the idea and I wouldn't be surprised if there ends up being more to it - but right now Gaye seems to pop up at times convenient for confessional narrative in a way that does not have me convinced.