Most exhibitions of the great from the past are impersonal affairs. There are statues, coins, plinths and papyrus fragments. They leave you interested but cold.

But the statues, coins, plinths and fragments that make up the British Museum's superb Hadrian: Life, Love, Legacy summer exhibition feel alive with the spirit of the great emperor himself. That said, it is still hard to make out the person.

The sense of presence is helped by the fact that you enter the exhibition beneath the fabulous dome of the round reading room, a building that is a direct descendent of Hadrian's masterpiece, the Rome Pantheon. You are greeted by what is surely the star piece of the show, a monumental head - as above. Less than a year ago it was still in the ground at Sagalassos, Turkey. This is first time it has been seen in public anywhere.

The sense of connection with Hadrian deepens when you hear that one of his first acts as emperor was to withdraw from an unwinnable conflict in what is now Iraq. (I saw David Aaronovitch at the press preview this morning, a British columnist and long-standing supporter of the contemporary war: my bet is on his next comment protesting at that parallel.) Indeed, the conflicts that Hadrian had to deal with are all in the same parts of the world as the conflicts our leaders today must handle. The parallels are quite explicit.

Then there is the earlobe crease that Hadrian had, clear in nearly all the busts of him. (It's just in the shadow of the photo I took above, though I like this head since it seems more personal than many of the stylized images, what with its thin lips and slight frown.) Such a marking is associated with congenital heart disease, and probably reveals how he died. Seeing the crease evokes sympathy for the man, deepens the sense of his humanity, and reminds you that even the great are dust and shall return to dust. This is the museum exhibition as religious experience, a trademark of the British Museum's director, Neil MacGregor.

Was Hadrian a thinker, even a philosopher? He would have met philosophers throughout his life, including Epictetus, Secundus the Silent and Herodes Atticus, the Sophist. The exhibition questions the philsophical credentials of the man, though, for all his undoubted aesthetic and architectural ability and taste.

The dark side of imperial rule is very evident too. There are objects belonging to Jews who undoubtedly died when Hadrian put down the Jewish Revolt of 133-135 CE. One is a papyrus inscribed with an order directly from Simon Bar Kokhba, though if a freedom fighter he was no pussy-cat. The threat of severe punishment to his supporters for disobeying him is underlined no fewer than three times in what is only a handful of words.

There is a section devoted to Hadrian's devotion to Antinous, including the statue above showing the deified Antinous as Aristaios (notice the full lips and large nipples). Strangely, though arguably the most personal part of Hadrian's life that we know about, this is perhaps the least moving part of the exhibition. There is also a note on how homosexual relationships were perfectly acceptable in ancient society, so long as the older male, or erastes, remained active over the passive youth, or eromenos. This economy of love is, though, today seriously questioned.

Towards the end, you come to a short excerpt from Hadrian's Autobiography, written on the only surviving fragment. It looks like a writing exercise with Hadrian's text being copied by a student, a sign of how widespread the document circulated in the second century, though now all but lost.

And it ends with the words from a poem the emperor penned, a suitably melancholic note:

Little soul, little wanderer, little charmer, Body's guest and companion, To what places will you set out now? To darkling, cold and gloomy ones - And you won't be making your usual jokes.