We all know the wall: that long line of stone that rises and falls across rough northern landscapes. It is one of the wildest and loveliest of our tourist spots. But the Romans who once paced its bleak ramparts with their spiked wooden pila were protecting the northernmost perimeter of the world's greatest empire: the empire that - stretching from Scotland to the Sahara, from the Atlantic to the Euphrates - was ruled from AD117 to AD138 by Hadrian.

But what do we know about him? The British Museum, fresh from a success in which a posse of terracotta warriors ousted Blackpool Pleasure Beach from the top of our list of favourite cultural attractions, now turns its attention from China's first emperor to another great wall-builder. In Hadrian: Empire and Conflict, it invites us to speculate on what this most fascinating and complex emperor might really have been like.

This is a show that Gordon Brown should go to see. It follows the progress of an ambitious but prudent second-in-command who finally gets to power by being adopted by his predecessor, the Emperor Trajan, on his deathbed. But leadership, Hadrian discovers, is far from plain sailing. Trajan may have been a warrior hero, but things were very over-stretched. Although the effects had not yet reached the public, the empire had been brought almost to breaking point by a war in the Middle East.

Hadrian was no ditherer. He dealt with the problem decisively. He ordered a swift withdrawal of troops in what was only the first of the many military, legal and economic reforms that, over 21 years, this emperor was to effect. The historian Edward Gibbon may have interpreted his retraction as the moment that the rot set in, but the final decline of empire was still a long way in coming and Hadrian's political wisdom, along with his cultural contributions (most prominent among them his architectural prowess), have left him with a reputation as one of the world's finest leaders. His achievements were outstanding. His legacy was immense.

The British Museum now assembles a spectacular show whose exhibits range from the heftiest stone pieces to the most fragile slips of papyrus with anything from portrait sculptures, through stone inscriptions and architectural models, to coins and mosaic pieces in between. Invest in the catalogue. It is a model of clarity, lavishly illustrated and relatively brief. It is the tiny details that snag the imagination: the tiny crease in the ear of Hadrian, for instance, that, apart from suggesting that he might have suffered from coronary artery disease, add a realism to the images that scattered his vast empire. Sometimes the plainest-looking exhibits carry the most momentous stories. In a stone inscription the name Syria-Palestina is used instead of Judea for the first time.

Sometimes the impact of pieces will be immediate and startling. As you look into the faces of a series of painted “mummy portraits” you feel you are staring into the eyes of the subjects that Hadrian (who, spending more than half his reign on journeys throughout the empire, must have met more of his subjects than any ruler before him) encountered. Other objects need more imaginative work. A length of lead piping must stand as a metonym for the luxury of the incredible villa at Tivoli.

Among the most appealing sections of this show is that dedicated to Antinous, the beautiful Greek boy with whom Hadrian fell in love. Curators let the museum's wonderful silver Warren Cup with its flagrant scenes of sodomy set the stage for a liaison which at that time was considered quite normal. What was odd, this show suggests, was the cult that ensued after Antinous' death in a Nile flood. The mourning Hadrian not only founded an entire new city in his honour but commemorated him in various god-like incarnations including as the Egyptian deity Osiris, who (complete with perfectly polished pectorals and loincloth bulge) meets the visitor at the entrance to this show.

Was it the depth of his grief that made Hadrian create this gay icon? The exhibition suggests another slant. Hadrian, the first emperor to sport a full Greek-style beard, was nicknamed “the Greekling” for his love of Hellenic culture. Now by celebrating this passion through the apotheosis of a Greek boy, he kept a potentially rebellious sector of society safely pacified. He made the Greeks feel an appreciated part of his empire. It was an adept political move.

Hadrian is certainly most often commemorated (in contrast to his warlike predecessor) as a cultured philosopher. He pops up again and again in this show in his many magnificent sculptural incarnations: as the toga-clad priest, the barbarian-trampling commander, the bearded peacemaker, the mighty benefactor. Which was the real person?

Our stock picture is that of the robed thinker. But the sculpture that propagated this image is re-examined in this show. The portrait head, it now appears, does not actually belong to the thinker's body. They have just been stuck together by mistaken archaeologists. This sculpture becomes a metaphor for an exhibition that sets out to break down the accepted image into its component parts and then reassemble it again.

The most haunting part of this show is that which displays objects found in the so called “cave of letters”, a rocky crevice in a parched wadi into which a group of Jewish civilians crawled. They hid there from the Romans, who were putting down their revolt with peculiar force. Here, perfectly preserved by the dry desert climate, are the objects that they salvaged before they fled, including the keys that they must have kept, hoping that they would return to their houses. They never did. They all perished. Hadrian the supposed peacemaker was also the perpetrator of a massacre that left hundreds of thousands Jews dead. And this - the only massacre for which we have written evidence - must presumably stand in as proof of the many rebellions that he quashed, including at least two in Britain.

This show has a spacious and unhurried feel. Each item is given the opportunity to speak. And the exhibition finds a particularly evocative setting in the specially adapted space of the museum's round reading room, the dome of which is a direct reflection of the Pantheon, whose spectacular rotunda - the largest un-reinforced concrete dome in the world - Hadrian pioneered.

The Pantheon was constructed as a forum for the emperor. Now, in an exhibition that occupies its 19th-century descendent, Hadrian once more discovers a stage from which to speak. The questions he asks resonate today. What price do we pay for peace?

Hadrian: Empire and Conflict is at the British Museum (020-7323 8299), July 24-October 26

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