When J Robert Oppenheimer first saw the awful power of the atomic bomb, in the Trinity test at Los Alamos, New Mexico, in 1945, he was reminded of the words in the Bhagavad Gita, "Now I am become death, the destroyer of worlds". Or was he? This famous anecdote actually comes from a documentary made two decades later. At the time, according to the physicist Isidor Rabi, who was there, Oppenheimer was openly triumphalist. "I'll never forget his walk," Rabi recalled. "I'll never forget the way he stepped out of the car his walk was like High Noon this kind of strut. He had done it."

The tension between Oppenheimer's two sides  his need to be at the centre of power versus his wish to retain his conscience  lie at the heart of Ray Monk's wonderful new biography. Monk takes as his starting point Isidor Rabi's assertion that Oppenheimer's problem was "identity": that he was "a man put together of many bright shining splinters", who "never got to be an integrated personality" "You carried on a charade with him. He lived a charade."

Oppenheimer was ill at ease with his Jewish origins, and thanks to his father's huge wealth and his mother's overprotective instincts he had grown up in a luxurious apartment on New York's Riverside Drive, surrounded by Van Goghs and Picassos and shielded from reality. In his own words, he was an "unctuous, repulsively good little boy", unprepared "in any way for the fact that there are cruel and bitter things", and he was offered "no normal, healthy way to be a bastard". This wouldn't have mattered had his ambitions not taken him into the big, bad world.

Oppenheimer's intellectual brilliance was never in doubt. He switched from chemistry to physics at Harvard, and after a disastrous interlude at Cambridge he plunged into the world of quantum mechanics, soon establishing himself as a theoretical physicist respected by  if not quite on a par with  Paul Dirac, Werner Heisenberg and Niels Bohr. At Berkeley in the 1930s he built up a distinctively American school of physicists and made contributions to astrophysics that, Monk argues, would have won him the Nobel prize had he lived longer.

Then came the two events that would shape Oppenheimer's life. In the late 1930s he began to associate with communists, unaware that they were under surveillance, and Oppenheimer himself popped up on the FBI's radar. And in 1942 General Leslie Groves, the man tasked by Roosevelt with building an atomic bomb in America, chose him to be the scientific director of the Manhattan Project. At the specially created laboratory at Los Alamos, Oppenheimer revealed extraordinary gifts of leadership, nursing a huge team of scientific prima donnas with passion, tact and skill.

With the dropping of the bomb, Oppenheimer became America's most famous scientist, but he was appalled by the human suffering at Hiroshima and made confused attempts to avoid an atomic arms race, which put him increasingly at odds with the hawkish mood in Washington. When he told Harry Truman that he felt he had blood on his hands, the president warned his aides to keep this "cry-baby scientist" away from him. Matters came to a head when Oppenheimer initially opposed the building of the "Super", or hydrogen bomb. His many powerful enemies  notably Edward Teller, the scientific advocate of the H bomb, the US air force and the Washington power broker Lewis Strauss  finally struck at him in 1954, using as their main weapon FBI records of his contacts with communists. They failed to prove that Oppenheimer was a Soviet spy, but they destroyed his character. He retreated to Princeton, where he ran the Institute for Advanced Study, before dying of throat cancer in 1967.

Monk retells this great 20th-century tragedy magnificently, in measured English prose, not Time journalese. He brings off the set pieces, such as the Trinity test, but he also explores Oppenheimer the physicist with a thoroughness some readers may find arduous. He is, though, surprisingly lacking in low curiosity, declining to speculate, for example (as the scientific writer Jeremy Bernstein does), on whether Oppenheimer's much disliked wife, Kitty, was the first woman with whom he had a full sexual relationship.

Inside the Centre shows how the passage of time has shifted perspectives. The FBI's obsession with Soviet atomic spies is more understandable now that we know how many of them there were. Equally, the scientists were right to foresee that the US could never hold the "nuclear secret" and that nuclear weapons would usher in a new age of mutually assured destruction. And yet they were naive to think that one could deal with Stalin. As Truman's secretary of state Dean Acheson said, "How can you persuade a paranoid adversary to disarm 'by example'?"

Oppenheimer himself has become less heroic and more fallible over time  a man who betrayed friends to hang on to his special position and lied in tight situations (though it was his misfortune to have his every human failing recorded and picked over for decades by security men, journalists and historians). It was inevitable, in the hysterical climate of McCarthyism, that Oppenheimer would be edged out; but his special facility in making enemies, the casual arrogance with which he had humiliated the powerful, guaranteed their revenge should take such a horrible form. If all the "evil of the times" was wrapped up in this judicial travesty, so were Oppenheimer's deep flaws of character.

Robert Oppenheimer was a complicated man. Everybody who knew him thought he was complicated; many of his friends and colleagues reckoned that he was far too complicated to figure out; some thought that he never figured himself out and that his life was one long, painful and ultimately unsuccessful experiment in personal identity, starting with toe-curling problems about sexual identity and culminating with mature, whose-side-is-he-on experiments in political identity.

Oppenheimer was a theoretical physicist. His best work was on the theory of neutron stars, and the fact that he never won a Nobel prize has been ascribed, variously, to his death in 1967 before the astrophysics research done in the 30s could be properly recognised and to his lack of intellectual focus: he was one of the last of the ancients who "knew too much".

But he is best known by far as the "Father of the A-Bomb", the scientific director of the Manhattan Project that designed the bombs dropped on Hiroshima and Nagasaki, an enterprise that he sometimes described as engineering, nothing to do with science proper. After the war, his resistance to a crash programme constructing an enormously more powerful hydrogen bomb and his support for international control of atomic energy were linked by cold war red-hunters to communist leanings. Edward Teller, the "Father of the H-Bomb", told the FBI in 1952 that, although he himself did not (of course) credit it, "a lot of people believe Oppenheimer opposed the development of the H-bomb on 'direct orders from Moscow'." The 1954 hearings that resulted in the withdrawal of Oppenheimer's security clearance transformed him into the tragic hero of the American left. Yet, beginning early in the wartime Manhattan Project, he repeatedly "named names", betraying students, close friends, and even  possibly  his own brother.

Appointed to lead the scientific work of the Manhattan Project in 1942, Oppenheimer was considered a bizarre choice. There was nothing in his background to indicate that he had the abilities to lead the biggest techno-scientific project in history. One of his colleagues joked that Oppie  as he was universally known to friends and colleagues  couldn't even run a hamburger stand, still less a large and complex organisation: he was temperamentally volatile, patronising and inept in his social relations, and thoroughly impractical. However, at Los Alamos, where the bomb was designed and assembled, he rapidly metamorphosed into a marvellously efficient and charismatic administrator. The greatest physicists in the world were assembled at Los Alamos, and their egos were immense, but they were lavish in their praise of Oppie's personal contribution: "He was very close to being indispensable."

Personal contradictions were one reason Oppenheimer was so difficult to take the measure of; the astonishing range of his interests and capacities was another. A sickly and cosseted child of immensely wealthy secular German Jews from Manhattan's bijou Riverside Drive, he became a chain-smoking, hard-drinking Marlboro Man, capable of reckless acts of physical bravery, riding horseback over vast distances in New Mexico's high desert wilderness and sailing his boat in dangerous conditions in Long Island Sound. Fluent in the literatures of the major European languages, he began lessons in Sanskrit so that he could study the classic Hindu sacred texts in the original. Soon afterwards, he wrote to his younger brother annoyingly announcing that reading the Bhagavad Gita was "very easy". At the instant the atomic age began, with the Alamogordo test, many bomb-builders could think of nothing grander to say than "It worked." Oppie's response was characteristic: he later recalled that what then went through his mind was a line from the Gita: "Now, I am become Death, the destroyer of worlds."

Oppie was a dreadful show-off. Some colleagues were irritated by the bar mitzvah boy displays; some regarded his breadth of learning as unimpressive. His friend II Rabi said that Oppie's "problem" was that he was "over-educated" in fields that had little to do with science, that he was too cultured for his own good. Emilio Segrè sneered at Oppie's intellectual peacocking, judging that his "celebrated general culture was not superior to that expected in a boy who had attended a good European high school", and finding Oppie's "ostentation slightly ridiculous". Still others, however, considered that his cultivation was genuine and that it was consequential for Oppie's authority among the Los Alamos scientists and, later, in American cold war culture. His polymathy, his philosophical sensibilities and his cultural cosmopolitanism counted for much, notably among the European émigré scientists. An English physicist wrote that they "needed a great gentleman to serve under", and the psychologically volatile Jewish boy from the Upper West Side turned out to be that gentleman.

Oppenheimer isn't an easy biographical subject: the complexity, the contradictions, and the cultural breadth provoke interest in the man, while for the biographer they constitute massive practical problems. Do you cut some aspects out and treat what remains? Oppie as bomb-builder? Oppie as witch-hunters' victim? Oppie as physicist? In fact, he did very little physics research after the war, and none at all after 1950, so why not figure Oppie as a cold war cultural commentator, giving as much weight to the oracular essays of that period as to the physics he produced over the 20 years of his active research career? Hans Bethe once said that Oppenheimer "worked at physics mainly because he found physics the best way to do philosophy," and Wolfgang Pauli observed that Oppenheimer "seemed to treat physics as an avocation and psychoanalysis as a vocation." The remarks were intended to be flippant but they were not obviously untrue.

Ray Monk recommends his biography over existing full-length accounts because it, uniquely, puts Oppenheimer's physics research at the centre of the narrative. It does do that, but it's not obvious that this is a privileged way of understanding, as Monk says, "Oppenheimer himself". It's striking, in this connection, that an account of the man "himself" has so little to say about Oppie's evidently difficult marriage  a colleague said it "looked like hell on earth"  and lets pass, almost without comment, an extraordinary episode at Los Alamos when Oppie offered up his new-born daughter to a friend for adoption. (The daughter hanged herself in 1977 and her older brother is a carpenter and contractor in New Mexico, occasionally engaging in anti-nuclear activism, who refuses to talk about his famous father.) Monk's biography privileges the physics and neglects the family  and maybe Oppie did that too.

Monk takes up Oppenheimer after having produced two of the greatest philosophical biographies of recent years. The towering achievement was a life of Wittgenstein and the other was a less sympathetic, but still extraordinary, two-volume study of Bertrand Russell. These biographies were philosophical not just because they were accounts of philosophers' lives and works but also because, as Monk has elsewhere reflected, biography can itself be a genre of philosophy. Wittgenstein wrote about "the kind of understanding that consists in seeing connections," the way you see "family resemblances" in a group portrait of related people, or the way you might come to just see a unified personality in an individual's disparate deeds and thoughts. Biography, in this mode, is the sort of non-theoretic knowing that Wittgenstein described and commended.

Seeing Oppenheimer whole is as hard as it gets. Rabi thought the key was that Oppenheimer constantly worked to convince himself and others that he wasn't really Jewish: it would have been better for him, the confidently Jewish Rabi said, "if he had studied the Talmud rather than Sanskrit  It would have given him a better sense of himself." Monk agrees that Oppenheimer's exquisite discomfort in his Jewish skin is a plausible solvent of the apparent tensions and contradictions, but he has several other candidates for seeing coherence. One is a less than whole-hearted suggestion that Hindu spirituality and metaphysics were serious bases for both scientific work and moral postures; another is a well-made case for the depth and pervasiveness of Oppenheimer's patriotism, his "deep, and sometimes fierce, devotion to his country"  a patriotism which saw America as the unique place where Jews could be free, which informed Oppie's attachment to communism conceived as a pure form of American egalitarianism, and which may have underpinned his ambivalent love-affair with the military. Monk's master-story, however, has Oppenheimer striving always to move from the margins of any enterprise in which he was engaged towards somewhere "inside the centre". But that's the least persuasive strand in this otherwise superb biography: who doesn't want to be somewhere near the centre of things?

Oppie once offered some advice to his younger brother who, he thought, had overestimated "the inconstancy and incoherence of personal life": "There is, there should be, and in mature people there comes more and more to be a certain unity, which makes it possible to recognise a man in his most diverse operations, a kind of personal stamp." That unity is what Monk tries to achieve for his subject, and that Oppie tried, and largely failed, to achieve for himself.

 Steven Shapin's Never Pure is published by Johns Hopkins.