 In 2008, at a Downing Street reception, Gordon Brown presented a young man, a member of Plane Stupid, with a Transport Campaigner of the Year award. During the ceremony, the young man superglued himself to the premier's sleeve. The prize is sponsored - ?10,000 a year - by Simon Phillips Norton, a rich recluse and public-transport obsessive who lives, surrounded by timetables, ticket-stubs, packets of Batchelors Savoury Rice, in a run-down multi-occupancy house in Cambridge. a former child prodigy, he is still believed to be one of the world's great living mathematicians, although he hasn't held down an academic position since 1985, when he was 33. and he used to be alexander Masters's live-in landlord, which is how he comes to find himself the subject of this book.  "I don't like your books, alex," Simon says in the epigraph to one of Masters's chapters. "Your representation of me as interesting is inaccurate," he says in another. "You must be very careful not to jump to easy answers," says John Horton Conway, a fellow mathematician. "Oh dear, I have a feeling this book is going to be a disaster for me," Simon comments in the epigraph to the book.  Masters's first book was Stuart: a Life Backwards (2005) won the Guardian first book prize. Masters told the story of how, as a mathematics postgraduate at Cambridge, he got a part-time job at Wintercomfort (a drop-in centre for homeless people, where a director and a manager were jailed in 1999 for allegedly allowing drug-dealing on the premises). Clients, staff, friends campaigned to support them: and so, Masters found his lot thrown in with Stuart Shorter, a young man struggling with a past that included heroin, Largactil, solvents, progressive disability and repeated childhood rape. The book had in it press cuttings, Masters's own Ronald Searle-ish line drawings, and Stuart's running commentary on the work as it went: "It's bollocks boring . . . Nah, alexander, you gotta start again." Polyphonic and reticulate, warm and harsh and very funny, the book was a triumph, a brilliant piece of authored documentary. Stuart died in 2002 before it was finished - the coroner recorded an open verdict after he stepped in front of a train.  Like Stuart, The Genius starts with Masters finding himself unexpectedly intimate with an unusual person. (In fact, Simon had a walk-on part in the earlier book - "Twice winner of a Mathematics Olympiad gold medal, co-author of atlas of Finite Groups, my landlord is a generous, mild man, as brilliant as the sun" - "One fact to get right, and you got it wrong in four different ways," Simon protests in the present one.) and as with Stuart, Simon's story is presented in an engagingly open-textured and multivalent way. There are photos of his mother, brothers, the family business. There's an exam report from Eton: "!!" is all it says for maths. There are Masters's own drawings, animating the basic principles of group theory, the area of maths that was Simon's passion. There's the newsletter Simon now edits for the Cambridgeshire Campaign for Better Transport. There's a picture taken by Masters of Simon himself, smiling broadly, holding up a tin of John West mackerel fillets in sunflower oil.  as you can imagine, much of this is delightful - the bloggy, scrapbooky aspect, the kipple and backchat and disgusting food. In her still-unsurpassed The Last Samurai - another tale of childhood prodigiousness - the novelist Helen DeWitt imagines "the writers of the future" learning to do with words what Cezanne and Schoenberg were doing close on a century ago with painting and music, and in its best moments Masters's work has something of that excitement, something new and open and risky and humane. The drawings, for example, depicting the basics of group theory: rows and ranks of squares rotated through 90, 180, 270 degrees, apparently unchanged, if it were not for the way the moves are represented, with flailing little humanoid arms and legs - a lovely insight into the synaesthesia of giftedness. "Mathematics was simply there: the setting for existence; the touchstone for all activity. It was to Simon what green fields and dark woods were to other schoolboys: the enjoyable places that you rushed to, whooping, as soon as the afternoon bell rang."  Other bits, however, get whimsical and overegged. So yes, the squares are nice - but was it really necessary to invent "Saucy Miss Triangle" with her high-heeled shoes and bloomers? I could also have done without the chapter printed in white on black (because it's dark in Simon's basement) and the joke about calling him "Simon MINUS Norton" (because he features not as presence but as absence, ho ho). and the bit with Masters imagining himself turning into his subject - there's a picture of him going to a party dressed up as the number 7.  also, there's something odd about the book's subtitle - The Biography of a Happy Man; call no man happy until he's dead, the Greeks used to say, and surely they were right. Of Masters's many virtues, the topmost is the way he refuses easy copout labels for a tricky person, his commitment to human variety and unfathomability. No matter what dreadful things Stuart did or what horror he suffered, he was not to be mollycoddled or monstered or let off any hooks. Simon's life - externally at least - does not appear so abysmal. But to call a person "happy"? Doesn't it soften the edges, dismiss the reality of a person's struggles, render a grown man cuddly and belittled, like a sort of gonk?  Besides which, if Simon's really that "happy", why does he keep talking about grief? "It's a cliche that mathematicians are over the hill by their mid-30s, but often it's not loss of mathematical intelligence that weakens their ability, but loss of  