Sometimes a man’s appearance can be misleading. This one is about 5ft 9in tall, not especially powerful in build; he has ears that stick out and teeth that seem too big for his mouth and he walks with a slightly asymmetric tilt. Yet this is General David Petraeus, the warrior whose “surge” saved America from a humiliating scuttle out of Iraq and who is now the head of United States Central Command (Centcom).

Only when Petraeus engages in conversation does everything snap into place. Each of his words is chosen with painstaking precision and the gaze is similarly well directed. Above all there is a sense of restless intelligence; so perhaps it is not so extraordinary that this 56-year-old soldier has been named the world’s leading public intellectual by a panel nominated by two prominent magazines of the thinking classes, Prospect and Foreign Policy.

The winner’s citation declared: “The so-called ‘Petraeus doctrine’ is the only written piece of intellectual output in the last two years that has made a direct difference to the lives of millions. It is the first actively humane warfighting doctrine to come out of the Pentagon, enshrining the idea that winning a modern war requires ensuring the security and wellbeing of the civilian population. Petraeus has also waged a war of ideas against many in Washington who argued that fewer constraints and more ruthless tactics were required in Iraq.” And, it points out, he won.

Petraeus, who tells me that “the most powerful tool any soldier carries is not his weapon but his mind”, has the distinctive battle honour of the intellectual, namely a PhD. His was won in the examination halls of Princeton, with a 328-page doctoral dissertation entitled The American Military and the Lessons of Vietnam.

It seems Petraeus drew precisely the opposite conclusions from the Vietnam war to those drawn by the likes of General Colin Powell. Powell believed that the US army should become a machine that delivered a massive, technologically awe-inspiring military punch at high speed but would not get involved in “nation-building” or the “messy stuff”. In contrast, Petraeus believes that “we don’t get to choose what kinds of wars we fight” and that the lesson of Vietnam is not that the US army should avoid counterinsurgency, but that it should become much better at it. Petraeus’s Princeton dissertation of 1987 also forecast that this would be made necessary in any case by “the rise of terrorism”.

Cometh the hour, cometh the man. When the situation in Iraq had conclusively demonstrated the limitations of US firepower divorced from human intelligence and political know-how, Petraeus’s doctrine of pouring men on the ground into the homes of those most threatened came into its own.

When I first met Petraeus, three months ago, he showered me with page after page of his “doctrine”, notably the “counterinsurgency guidance”. Rule 3 is: “Money is ammunition.”

This was certainly central to the surge’s success: Petraeus put 100,000 or so gunmen from the Sunni militia on the payroll in return for their help in slaughtering Al-Qaeda fighters. It seems almost certain that he will implement a similar strategy in Afghanistan against the resurgent Taliban.

Other phrases that leap out of the presentation Petraeus gives me are less redolent of the black arts. They contain such advice to his troops as, “Live among the people. You can’t commute to this fight”; “We cannot kill our way out of this endeavour”; and “Walk. Work dismounted. Stop by, don’t drive by. Awareness can only be gained by interacting face to face, not separated by ballistic glass”.

In the earliest stages of the surge Petraeus gave his security detail conniptions by acting on his own advice and taking off his helmet when walking through villages still harbouring those who would have liked nothing more than to have killed a US general. This is where Petraeus the intellectual morphs into Petraeus the man of action – after all, his slightly tilted gait is not eccentricity but the legacy of a malfunctioning parachute and a resulting crushed pelvis.

When I call the general to congratulate him on his award, I ask him whether he is missing the field of combat, now that he is based at Centcom headquarters in Florida. “Yes, there is something undeniably – and I hope your readers don’t misunderstand this – exhilarating about being in combat. That is, until you get the casualties, the damage, the loss.”

Although Petraeus is now associated indelibly with the US’s attempt to “nation-build” in Iraq, don’t forget that in 2003, as a major-general, he commanded the 101st Airborne Division, which undertook the longest helicopter assault in military history. Has he become in any way hardened as a result of these experiences? “If you mean: did I get hardened to losses, to casualties, I never found that I did. They never got any easier to accept. You have to keep thinking about it, otherwise it’s as though the casualty reports are like water poured into a vessel with holes, and it shouldn’t be like that. I would make a point of going personally to the memorial ceremonies whenever possible and certainly when there were multiple losses.”

There is, he says, a paradox to soldiering that no commander can afford to ignore. Peacekeeping just isn’t as inspiring as the rough stuff. The level of violence in Iraq has, he says, come down sharply since the surge. “In one day in June 2007 there were 180 attacks on coalition troops, but in the last month or so it’s been down to around 10 a day.” And while this is evidently good news, it also brings problems.

“The company commanders I talk to will often say that, in the last six months or so, we’re dealing with the challenge that soldiers can’t get as fired up about, say, the restoration of fish farms or poultry industries or local market revival as they can about true combat operations. So they need to be reminded what happens when you have real operations: there may be an adrenaline moment . . . but it’s often the moment after which some of their buddies and they might never be the same. And so it is paradoxical.”

Petraeus concludes with the observation that “Sherman had it right about war”. He is, of course, referring to the much-quoted remark made by General William Sherman, the great American civil war leader, to a graduating class of the Michigan Military Academy: “There is many a boy here today who looks on war as all glory, but, boys, it is all hell.”

Petraeus compares America’s soldiers of today to their forefathers who fought the second world war. They were called “the greatest generation”, he says, but the young warriors of the Iraq campaign “should be called the new greatest generation”.

It’s an interesting comparison – even if, as I point out, the public will always find it easier to acknowledge and appreciate the sacrifices made by the second world war generation. The fight to destroy Nazism is one thing; a deeply controversial preemptive invasion quite another.

Petraeus gives a little sigh: “Ever since I came back from my first tour of Iraq, people have asked me: was this the right thing to do? I said then that this would have to be left to history and I still firmly believe that. However, I do think it is fair for soldiers to ask whether their sacrifice has been meaningful. Without going back into the whole difficult question of Iraq, the decision to go to war and so forth, I think the Iraq that is emerging now, for all its imperfections and flaws, is encouraging to those who have given so much.”

This hedged and equivocal assessment may suggest that Petraeus is filled with more misgivings about the whole Iraq enterprise than he would like to express in public; but even if he were secretly to share the view of Barack Obama that the war was not justified, he does not seem sympathetic to the president-elect’s stated position that US troops must leave Iraq within 16 months of his taking office.

When I ask Petraeus whether this is a sensible or reasonable objective on thepart of his future commander-in-chief, he notably avoids saying “yes” and gives a carefully constructed response. “What we are looking forward to is a discussion between the senior elected leader and the military advisers. It starts with a discussion of objectives, and this is what the dialogue must focus on first. That is, what are we seeking to achieve in Iraq and in the region? All of these things have to be looked at regionally.

“One of the big points about Afghanistan, for example, is that you can’t grapple with that issue solely in Afghanistan; obviously you have to include Pakistan, and you have to look more broadly than that, at India and China, Iran and a host of other countries. But you have to start by agreeing on the objectives, the mission, if you will, and the purpose of achieving the task.” In other words, he seems to be hinting, no merely political deadline should supersede the overall strategic objective.

In our conversation Petraeus finds an elegant way to describe the tensions that inevitably exist between politicians contesting electoral campaigns and generals who fight on a less ephemeral battleground. He observes: “Al-Qaeda and its allies are keenly aware of the strategic context in which they operate. They are very aware of the Washington clock, the Nato clock, the London clock.

“I have to tell you that I sometimes thought that the Washington clock was running a lot more rapidly than the Baghdad clock – occasionally you had to tap the Baghdad clock to make sure that it was still ticking. So, again, an awareness of Al-Qaeda’s appreciation of the global context, and its resilience, must be considered as we craft and refine our strategy.”

The “London clock” is certainly ticking fastest: last month Britain confirmed that it would be withdrawing all its troops from Iraq by May. When he was interviewed by a British newspaper a year ago, Petraeus expressed the wish that America’s British allies in Iraq would “continue in the in-together, out-together spirit that has characterised this venture”. Is he disappointed that the Brits have not so continued? “I don’t see it that way now, frankly, because where I am here, I’ve got a broader perspective, and I’m looking at the overall fight against extremism, which obviously encompasses Afghanistan. It would have been very different if the British forces had left when they were still hugely engaged [in southern Iraq] but . . .the Iraqi forces in Basra have actually begun to perform relatively credibly.”

Sometimes, when talking to Petraeus, he comes across so much as the politically astute intellectual that it is necessary to recall that he is first and foremost a soldier. So finally I ask why he decided to join the army.

“The first thing to say is that you are around wonderful people, who have raised their right hand as volunteers to put themselves in harm’s way for their country. Beyond that, I’ve always enjoyed the fact that in the military you start the day with physical training. I’ve always enjoyed running and other athletic activities.”

He’s not kidding. In 2007 Petraeus gave an interview to Runner’s World, whose reporter began his breathless piece as follows: “Gen David Petraeus has just challenged me to a push-up contest. A moment later he’s prone – ramrod straight, back and arms rigid. Then in a 90-second blur he hammers out 81 push-ups while deconstructing David Ignatius’s latest novel. How can anyone keep up with that?”

Fortunately Petraeus does not want to issue a physical challenge to this hopelessly unfit interviewer. Instead, he summarises his love of his chosen career by quoting, from memory, President Teddy Roosevelt’s great speech The Man in the Arena.

“The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly . . . and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.”

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