When Simon Norton was 3 1/2, his I.Q. was measured at 178. For three years running in high school, he was among the top scorers in the world at the International Mathematical Olympiad. At the age of 27, he and a colleague, John Conway, formulated an audacious conjecture in group theory called “monstrous moonshine,” which inspired a frenzy of mathematical work around the globe that culminated in a Fields Medal-winning proof by Richard Borcherds almost two decades later.

Today, Norton holds no paid employment, publishes in his field only occasionally, subsists largely on canned mackerel and rice packets, and spends much of his time riding buses around Britain in a campaign to preserve public transport against deregulation. He lives in the basement of a house he owns in Cambridge, renting out the upper rooms. By chance, one of his tenants is the writer Alexander Masters, whose heartfelt and eccentric book “Simon: The Genius in My Basement” chronicles Norton’s strange journey from prodigy to . . . well, to whatever he is now.

Masters rolls jauntily through Norton’s life history — his Sussex upbringing in a Sephardic family whose jewelry business bankrolls him to this day; his passage through an upper-crust boys’ school (complete with a contemporary appearance by a regretful former bully); and his early academic triumphs at Eton and Trinity College, Cambridge. These sections are interleaved with short lessons in group theory, the mathematical study of symmetry. Masters is notably deft at conveying the basic ideas in a friendly way (lots of cartoons) without overreaching. Group theory was Norton’s mathematical love: he’s best known as an author of the “Atlas of Finite Groups,” a heroic attempt to describe all the basic types of symmetry between one set of oversize covers. This was not even 30 years ago, but the very idea of a final reckoning now seems antique; these days we put such information online, where it can be endlessly corrected and improved. It’s been years since I hauled the big red “Atlas” from the top of the bookcase. (It doesn’t fit on a shelf.)

Masters’s book is in no way a conventional biography, thanks largely to the presence of Norton himself in all his feisty, mackerelly complexity. Masters hands drafts to his subject as he goes, then records the usually aggrieved reactions. Norton is especially hard on what he considers Masters’s oversimplified or meaningless attempts to explain the mathematician’s worldview. Norton is correct in all cases, and you have to admire Masters for allowing him the last word. In this way “Simon” reminded me of Ian Hamilton’s “In Search of J. D. Salinger,” which similarly sets out to be a biography but ends up, under relentless pressure from its subject, an altogether different kind of book, about the challenge of capturing an unwilling living figure in a dead paper medium. That problem, unlike the math problems Norton studied, has no solution. Specifically, “Simon” never really answers the questions that animate it: What happened to Norton? Why did he suddenly quit mathematics? All of Masters’s proposals in this direction are derisively rejected by his subject, whose own more pedestrian explanation seems mostly right: He suffered an unusual lack of flexibility that kept him from venturing beyond the narrow patch of group theory where he made his name, even when there was little left to be mined. (Norton also blames the psychic damage done him by the 1985 “Deregulation of the Buses Act.”)