First, both the facts and the legend:

In January 1913, the great English mathematician G.H. Hardy received a letter at Trinity College in Cambridge from a 23-year-old clerk, at the Port Trusts Office in Madras, named Ramanujan. Ramanujan included a dozen or so pages of formulae, equations, and suppositions, all without proof. Was this work, Ramanujan wondered, of value?

Hardy quickly recognized the astonishing quality of the materials. This was a mathematician of the very highest rank, he concluded, but unpolished, with little or no formal education. Hardy arranged for Ramanujan to come to Trinity College at once. A half-dozen years of intense and very productive collaboration followed.

Immediately after the war, Ramanujan returned to Madras, now a fellow of both Trinity College and the Royal Society, the latter the highest scientific and mathematical honor England could bestow. He died very shortly thereafter at the age of 33.

It is over the skein of this romantic and beguiling story that David Leavitt’s extraordinary novel “The Indian Clerk” (Bloomsbury, 496 pages, $24.95) plays.

Long, intensely detailed, and realistic “The Indian Clerk” employs all of the novelist’s craft to tell the story of Hardy and Ramanujan’s friendship and collaboration.

It is a novel that hews closely to the facts: Almost all of the book’s characters — who include not only Hardy, Ramanujan, and Hardy’s celebrated collaborator David Littlewood, but also, in cameo appearances, Bertrand Russell, Wittgenstein, D.H. Lawrence, and J.M. Keynes, and perhaps a half-dozen others — derive from the historical record. Numerous quotations come directly from primary sources, and I half expected an index of characters and endnotes; as it is, an excellent bibliographical essay helps us keep track of what is derived from historical materials and what Mr. Leavitt has invented.

Committed to the principle of verisimilitude, Mr. Leavitt’schoices as a novelist were thereby significantly constrained, particularly in plotting. Minor characters or the dates of various events could be altered as he needed, he invented dialogue, and imagined what his characters were thinking, but the general outlines of the story were set in stone, like the rhyme scheme for a villanelle.

The story, recounted from Hardy’s perspective years later, begins with Hardy’s reception of Ramanujan’s letter, and ends with Ramnujan’s death. In between, Mr. Leavitt has succeeded in writing a novel filled with drama: The subtle drama of mathematical creation, and the intensely nuanced lives of his characters fill the page and give “The Indian Clerk” its propulsive force.

Mr. Leavitt is an expert novelist and seeds in his historical details elegantly, from makes of cars and styles of dress to the recipes for vegetarian cuisine; in a particularly wonderful detail, the strictly Brahmin Ramanujan is served a vegetarian goose by his Cambridge hosts. Mr. Leavitt’s use of historical materials is never ostentatious, but every fact serves its purpose of faithfully re-creating another time and place.

“The Indian Clerk” is an unusually instructive novel, and I mean that in an entirely complimentary sense: The novel explains, among other mysteries, what the Riemann hypothesis is, how a working mathematician in the domain of number theory proceeds, how a Cambridge college is organized, and what one eats at High Table, what England in the grip of war felt like, why Bertrand Russell lost his position at Trinity College, how the Cambridge tripos in mathematics came to be reformed, and the history of the great Cambridge secret society known as the Apostles. I was grateful to learn these things.

And yet this is also every bit a book showcasing all the advantages of a novel over biography or history. Large swathes of “The Indian Clerk” play over mental spaces inaccessible to the biographer: We come away having passed significant time exploring the inner life of Hardy, a melancholy, brooding hero, his collaborator David Littlewood, and Hardy’s rival for Ramanujan’s affection, the wife of another mathematician. Ramanujan himself remains far more opaque, a deeply moving figure, but one which we, appropriately enough, never come to know intimately.

“The Indian Clerk” is also quite a page-turner — a small miracle in itself, given that we are told on the first page that Ramanujan will die, and when — but what a difficult novel this must have been to write!

Mr. Leavitt is an American and teaches at the University of Florida in Gainesville: All of his characters, with the exception of Ramanujan, are English. I am not English, but to my ear, every line of dialogue rang true; so often when an American writer writes English English, it feels forced, larded with inappropriate phrases such as “I say, old chap!” Not here, even with characters coming from all ranks of the English class system. Moreover, the inner lives of the characters feel particularly English: cramped and emotionally constrained, but also so very dignified and productive.

Even more difficult was Mr. Leavitt’s subject matter: mathematics and mathematicians. Mathematics is a discipline of great drama, but the drama is not always apparent to an audience unprepared to take up pencil and paper and slog away. Yet Mr. Leavitt manages to communicate — if never explaining exactly what Ramanujan and Hardy accomplished together, or why it was significant — that they did accomplish something significant together. Mr. Leavitt never asks us to slog, but I left the novel convinced that Ramanujan was a genius. Mr. Leavitt is interested in human beings and not mathematics: Ramanujan’s work with Hardy, which in real life ranged over every frontier of the discipline, is too difficult to include in a novel intended for a general audience, and Mr. Leavitt wisely limits his mathematical discussion to a few simple and accessible theorems in number theory.

Mr. Leavitt overcomes these problems splendidly. Any novel that opens up a world as this one does; which produces such admirable and interesting characters; a novel with no villains and yet great tension; which communicates the life of another era so effectively; and which in the end proves so moving — such a novel deserves sustained applause.

Mr. Berlinski lives in Haiti. He is the author of ‘Fieldwork,’ a novel (Farrar, Straus & Giroux, 2007).