“You know the story of the invention of the computer?” one character asks another midway through Jane Smiley’s best-selling 1995 novel “Moo.” The speaker, an animal scientist, dreams of striking it rich by pioneering a new dairy-farming technology. To that end, he hopes to pry major grant money out of the agricultural industry, and he wields the history of the computer as both cautionary tale and crowbar. “The short version,” he explains, “is that the guy at Iowa State who invented the computer in the late ’30s never patented a thing. . . . And the university . . . forgot about the old machine, and threw it out.”

Now, in Smiley’s new book, “The Man Who Invented the Computer,” we have the long version. The title character — the ­real-life “guy at Iowa State” — is John Vincent Atanasoff, a physicist and mathematician who invented the computer largely out of frustration. Anyone who has studied calculus knows that solving differential equations is a tedious process: labor-­intensive, error-prone, slow. That process grows more arduous as equations grow more complex, and by the 1930s, as Smiley recounts, the difficulty of calculation was impeding scientific advancement. In response, Atanasoff designed a machine to do what his own mind could not. “I did not want to search and invent,” he confessed, “but sadly I turned in that direction.”

Atanasoff’s device became known as the Atanasoff-Berry Computer, or the ABC — except that it hardly became known at all. In the technological pantheon, Atanasoff is overshadowed by the likes of Alan Turing, who laid the intellectual groundwork for the computer and helped crack the German Enigma code during World War II. And the ABC itself is overshadowed by Eniac, an early computer conceived by the physicist John Mauchly. Mauchly was not a better scientist than Atanasoff, but he was a more ambitious entrepreneur. In his patent application for Eniac, he and his fellow designer J. Presper Eckert claimed responsibility for more than 100 innovations. As Smiley puts it, they saw themselves not as “team members,” but as “stars and owners who stood to gain fame and fortune.”

In 1973, a judge invalidated the Eniac patents, ruling that Mauchly’s invention was based on Atanasoff’s innovations. That decision represents the climax of Smiley’s book. Yet to say that Atanasoff’s story concerns a disputed patent is like saying that “Bleak House” concerns a disputed will. It’s true, but it leaves out the rivalry, the betrayal, the mysterious death, the international espionage and, to top it off, the Second World War.