It is still the most powerful building in the world. Every time I walk inside – its vast, silent, columnless dome always a surprise after the hubbub of the city – I get goosebumps. If an Ancient Roman were standing right next to you, living, breathing, you’d think it a miracle. Yet slap-bang in the middle of Rome, surrounded by traffic, German tour groups and pigeons, is a piece of Ancient Rome still living, still breathing almost 2,000 years on.

People walk past the Pantheon as if it were part of the furniture, which, in a sense, it is. It is just another church in a city of a thousand precious churches. Inside, several times a day, gawping tourists are tactfully elbowed aside for services. At the end of the day, the building’s checkerboard marble and granite floor, softly pitted by generations of feet, is mopped by the caretakers, while outside, at night, its flanks of sooty ancient bricks are surreptitiously fly-posted to advertise Italian boybands. The Pantheon is a living part of the city, just as it has always been.

It seems all the more powerful because no record exists of its creator, its architect. We do, though, know who commissioned it, and whom some suspect even of having a hand in its design: the Emperor Hadrian, celebrated this month by a big exhibition at the British Museum.

In Britain, Hadrian’s name seems known only for the 73-mile wall that he had built to mark the outer limits of his empire. The exhibition, though, hopes to paint a more vivid picture of an emperor, according to one ancient account, “in the same person . . . niggardly and generous, deceitful and straightforward, cruel and merciful, and always in all things changeable”.

He was both an imperial paper-pusher of the most anally retentive kind – infamous for controversially ditching his predecessors’ policies of war and expansion in favour of a slightly unsexy combination of peace, consolidating territory and increasing administrative efficiency – and an aesthete, perhaps the most erudite, sensitive and sophisticated of all Roman emperors, well versed in poetry and painting, and a virtuoso in his greatest love of all – architecture.

Hadrian began work on the Pantheon as soon as he became emperor, in AD11718. Endowing the city with monuments to butter up the citizens had been a well-honed policy since Augustus. It was perhaps also driven by a need to escape the shadow of his predecessor and adoptive father, Trajan, who guaranteed popularity with the usual bread and circuses – wars, imperial expansion and a monument-building programme of then unprecedented scale with his architect, Apollodorus of Damascus.

Hadrian’s historical detractors claim that so bitter was he at Trajan’s posthumous reputation he had Apollodorus killed after the architect mocked one of Hadrian’s own designs. All myth, alas – indeed, one of the first acts Hadrian undertook as emperor was to honour Trajan and his sister with temples. Under his patronage, vast swaths of the city were restored.

Hadrian could lay claim to being the world’s first conservationist – passing laws curbing unnecessary demolition – and urban regenerator, involving himself in the minutiae of neighbourhood politics, and recognising the civilising effects on his populace of a decent, unpotholed pavement, laws banning heavy traffic and a good flood prevention policy.

And then there were his monuments: the Pantheon, that Temple of the Divine Trajan, the vast Temple of Venus and Roma, the only building for certain designed by Hadrian, his country estate at Tivoli and, to cap it all, his mausoleum – its ruins now assimilated into Rome’s Castel Sant’ Angelo. His wall in northern England was no exception, either. In the provinces, Hadrian bolstered defences, improved cities and built temples, along the way revolutionising the construction industry and securing jobs and prosperity for the plebs. Hail Hadrian, patron saint of hod-carriers.

Hadrian’s architectural passions were the high point of the “Roman Architectural Revolution”, 200 years during which a genuinely Roman language of architecture emerged after several centuries of slavish copying of the Ancient Greek originals.

At first the use of such novel materials as concrete and a newly rigid lime mortar was driven by the empire’s expansion, and the consequent demand for new large, practical structures – warehouses, record offices, proto-shopping arcades – easily and quickly put up by unskilled labour. But these new building types and materials also provoked experimentation – new shapes, such as the barrel vault and the arch – acquired from Rome’s expansion to the Middle East.

Hadrian was, in architectural matters, both conservative and audacious. He was infamously respectful of Ancient Greece – comically so to some: he wore a Greek-style beard, and was nicknamed Graeculus. Many of the structures he put up, not least his own Temple of Venus and Roma, were faithful to the past. Yet the ruins of his estate at Tivoli, with its technical feats, its pumpkin domes, its space, curves and colour reveal a theme park of experimental structures that are still inspirational.

But it was the Pantheon that stole the show. By now, the Roman construction industry was so sophisticated, with its mass production, standardised dimensions and prefabrication, this immense structure was put up in just ten years. It is a technical masterpiece. No dome this size had been built before – or for centuries afterwards. On deep concrete foundations, its drum rose in poured concrete layers in trenches faced with brick walls. The dome was poured on top of a vast wooden support, in sections that get lighter and thinner – though imperceptibly so to the visitor – as you ascend. Imagine the moment when the support was removed. Imagine then walking in for the first time.

Much has been written on the meaning of the Pantheon, its proportional or numerical symbolism – the pleasing harmony, for instance, of the dome’s height being the same as that of the drum on which it sits. Is the oculus, open to the sky, letting light pour in, a surrogate sun? Is the dome an immense orrery (model of the solar system)? All guesswork. Though it seems safely certain that this was meant as the centrepiece of Rome’s now united and peaceful universe, a temple to all the gods.

The mystery, combined with the building’s sublime simplicity, secured its reputation. Indeed the Pantheon has become the most emulated building in the world, its shape echoing in buildings from Jerusalem’s 4th-century Holy Sepulchre, through the Renaissance to the domed pavilions at Chiswick House, Stowe and Stourhead Gardens, to Smirke’s British Museum Reading Room – where the exhibition is housed.

At the back of its porch, there is an inscription put there by Pope Urban VIII in 1632: “The Pantheon, the most celebrated edifice in the whole world.” Hadrian’s edifice was beyond ordinary human reputation – dedicated to gods, but also, for the first time, to architectural pleasure for its own sake. He was rare among emperors for not inscribing his structures with his own name. He didn’t need to.