Twenty-five years ago the word "Turing" tingled with mystery for the few who knew it. Readers of Douglas Hofstadter learned that Alan Turing belonged with Gdel in exploring minds and logic and knew also of "the Turing test" for artificial intelligence. But others were aware of Turing as a British figure, a Cambridge mathematician, emerging in connection with the huge World War II operation to break the Enigma ciphers. His crucial importance in the battle of the Atlantic was still shrouded by state secrecy. In fact, it was only after this secrecy was lifted that he began to be acknowledged for another great contribution--his role in the origin of the computer.

The conspicuously missing feature was the testimony of Alan Turing himself. He had died at age 41 in 1954, apparently killing himself with cyanide--and leaving a jagged hole in history. By 1980 rumor told of the prosecution and punishment that he had undergone as a homosexual in 1952. But even then, such a story could no longer serve as a simple explanation of suicide. Turing's friends had known him as unashamed and contemptuous of convention. A different suspicion struck those who knew the dark side of the 1950s. The victorious Allies must have been appalled by this revelation of the man who knew their secrets: How could Turing's private desires be reconciled with the public demands of state security? But on this question, total silence reigned.

Since then, the situation has completely changed. A number of events have made Turing's life better known to the public than that of probably any other mathematician. A notable actor, Derek Jacobi, has played Turing's drama to millions of viewers in Hugh Whitemore's 1986 play Breaking the Code. Little is secret from Google, and computer science students may find themselves expected to assess his life and death. Massive U.S. government releases in the 1990s have made World War II code breaking the subject of detailed scholarship, and conferences and books celebrate Turing's continuing influence. Complexity theory and quantum computing build on his analysis of computation, and since the 1980s Roger Penrose has given new life to Turing's deepest questions. Above all, Turing's reputation is now solidly underpinned by the vindication of his vision. Although John von Neumann led by a few months in creating a computer plan, it was Turing who explained in 1946 how "every known process" could be turned into computer software. Turing had seen this prospect in the simple but revolutionary principle of his Universal Turing Machine, laid out in a paper in 1936, and had thus created an amazing link between the purest mathematics and the most productive industrial applications.

But there are always more secrets to unravel and always room for yet another introduction. A series of "great discoveries," such as the current undertaking from W. W. Norton, cannot ignore Turing, and it is interesting to see the story of his contributions attempted by an American novelist, David Leavitt. The story is not simply a question of dates and facts. To use one of Turing's own images, it is like the skin of an onion. It calls for a writer who can unpeel it with care and who is unafraid of tears.

Intensely private, yet relishing popular writing and broadcasts, fiercely proud and yet absurdly self-effacing, Turing led a strange life intertwined with characteristically odd British puzzles of class and lifestyle. A central paradox is that he asserted the "heretical theory" that the human mind could be rivaled by a computer, whereas his own personality so little resembled the output of a machine. It was willful, individualistic, unpredictable. His struggle to incorporate initiative and creativity in his artificial-intelligence theory is therefore a personal drama. This is a puzzle that goes to the heart of science and yet is also fine material for a novelist of insight.

Leavitt's focus is elsewhere, however. It is on Turing as the gay outsider, driven to his death. No opportunity is lost to highlight this subtext. When Turing quips about the principle of "fair play for machines," Leavitt sees a plea for homosexual equality. It is quite right to convey his profound alienation and to bring out the consistency of his English liberalism. It is valuable to show human diversity lying at the center of scientific inquiry. But Leavitt's laborious decoding understates the constant dialogue between subjective individual vision and the collective work of mathematics and science, with its ideal of objectivity, to which Turing gave his life.

Scientific content is not neglected; Leavitt's discussion of Turing's 1936 paper has perhaps excessive technical detail. But the vision is partial: he fails to give any discussion of what Turing's proof implies for the question of artificial intelligence. A general problem is that, being the prisoner of secondary sources, the author finds himself the outsider. He quotes from another writer on statistical methods in 19th-century code breaking but omits the primary fact that Turing's central scientific contribution at Bletchley Park, the British wartime cryptanalytic center, was his statistical theory of weighing evidence. The book's subtitle is "Alan Turing and the Invention of the Computer," but on the critical question of Turing's relationship with von Neumann it must rely on quoting Martin Davis's Engines of Logic.

This is no groundbreaking book, nor does it do much hoeing or weeding. It is a survey of a field long cultivated by other hands, devoid of new witnesses. The title, also secondhand, suggests new light on his death, but there are no new facts. Leavitt claims a "sad descent into grief and madness" induced by the prosecution--he ignores the heap of manuscripts from Turing's last prolific year of research and misrepresents his renewed interest in physics as ravings. No new revelation about Turing's code breaking is offered. Leavitt describes his visit to Bletchley Park--now a museum--but only as a tourist, to report the embarrassment of a tour guide in describing Turing's fate. In this book, Leavitt offers his own tour. It is one that many will find congenial and that will at least introduce new readers to the still tingling enigma of Alan Turing.