Every filmmaker and book illustrator knows how to depict an ancient Celt. A typical Celt is supposed to have been a hairy, mud-smeared hooligan dressed in ragged tartan. In a land of trackless forests beyond the edges of the Roman empire, those ignoble barbarians, inspired by bloodthirsty priests known as druids, conducted a futile campaign of resistance against the superior civilisation from the south. Violently nostalgic and rarely sober, they were easily outclassed by the super-efficient Romans.

The popular view of our Celtic ancestors would have been instantly recognizable to a Roman, based as it is on Roman prejudice. The Roman historian Cassius Dio claimed that the Celts of northern Britain lived off roots and bark and were capable of surviving for days on end in swamps with only their heads above water.

Even in the relatively civilised land of Gaul (which covered roughly the same area as France), Homo Celticus was barely human. He blundered into battle with his brawny, blue-eyed wife wearing either animal skins or nothing. At home, he drank undiluted wine and wore trousers instead of a toga. This was in the part of Gaul known as Gallia Bracata (‘Trousered Gaul’). Further north, in Gallia Comata (‘Hairy Gaul’), things were even worse. The natives’ table manners were atrocious. They had been known to fight to the death over the pork roast, and since Celtic aristocrats never shaved their upper lips, according to Diodorus Siculus, “their moustaches become entangled in the food, and when they are drinking, the beverage passes through a kind of a strainer”.

More than 2,000 years after the legions of Julius Caesar slaughtered and enslaved two-thirds of the population of Gaul, we still imagine the barbarian Celts lurking in the primeval squalor of their thatched huts, waiting for the Roman landlords to come and install the plumbing and the central heating. Yet, as archaeologists have known for some time, Celtic civilisation was one of the most advanced of the ancient world. At its height, it stretched from the Highlands of Scotland to the shores of the Aegean Sea and produced a dazzling array of artistic and scientific masterpieces.

In the sixth century BC, when Rome was still an obscure settlement on the lower Tiber, a Celtic princess lived in a wooden palace above the Seine in Burgundy. Behind the yellow-painted walls of her palace, she was surrounded by hi-tech luxuries and expensive foreign imports: her jewellery and tableware came from all over the known world. She had glass and amber beads from the Baltic, and a solid gold torc from the Black Sea. Her state-of-the-art chariot had wide-angle steering, and her wine-mixing urn from southern Italy could hold 1,100 litres of the red nectar.

By the time Caesar landed in Britain in 55 BC, even the northern Celts were living in warm, well-insulated houses. Some of their timber mansions were greater feats of engineering than any Greek or Roman temple. Wealthy Britons drank wine from glasses and snacked on Mediterranean olives. No doubt those luxuries were reserved for an elite, but the general standard of living was high. When the Greek writer Timagenes was conducting research for a history of the Celts, he was amazed to find healthy and elegant people wherever he went: “You will never see in all these countries a man or a woman, however poor, either dirty or in rags.”

These were not the savage tribes described by Caesar in his book on the Gallic War. Caesar knew that his readers in Rome wanted to hear tales of daring exploits in an untamed world, and so he boasted of epic marches through bogs and forests. In reality, he discovered a land of tidy fields and coppiced woods. Celtic agriculture was advanced enough to supply the Roman armies with the 100 tonnes of wheat they required for each day of the eight-year-long campaign.

Even the semi-mythical land of Britannia was surprisingly civilised – not that this is apparent from Caesar’s account: “The Britons fortify their tangled woods with a ditch and a rampart and call it a town.” He wrote to Cicero, who passed the information on to a friend: there was “no prospect of booty” from Britain, “unless you count the slaves – and you won’t expect any of them to be highly qualified in literature or music!”

The excavation of the Roman town of Calleva Atrebatum (Silchester) has revealed a very different picture. In 2011, beneath the remains of Roman Calleva, archaeologists found an earlier, British town or oppidum. It had a grid pattern of streets oriented on the solstice sun. This is one of the most important archaeological discoveries of the last few decades: the Romans can no longer take the credit for the first planned towns in Britain.

It is revealing that Caesar himself, instead of returning to Italy, spent the winter of 52–51 BC in a “large and well-supplied” Celtic oppidum in Gaul. It was at Bibracte, on the summit of Mont Beuvray, in a teeming town of shops and factories, that he wrote his book on The Gallic War.

Those comfortable Celtic towns were connected to one another by a vast network of roads funded by tolls. This is one of the many facts about the Celtic world that has been erased by Roman prejudice. Schoolchildren are still taught that there were no proper roads before the Romans, and that the Celts had to make do with winding, muddy tracks. Yet most of the settlements that stood along ‘Roman’ roads were there before the Romans… If there were no proper roads before Caesar, one would have to believe that the Celts thoughtfully arranged their towns in straight lines so that, when the Roman engineers arrived, they could easily join them all together.

Long before the Roman conquest, merchants were racing from the Mediterranean to the English Channel in under 30 days. Even in the 18th century, the same journey took only a few days less. Beautifully engineered chariots have been found in Celtic graves from Yorkshire to the Rhineland. Those sleek machines were clearly not built for rubbly trails. The Romans had been so impressed by Celtic carriages and carts when they first encountered them in the fourth century BC that they adopted the new technology and abandoned their own antiquated contraptions, which is why nearly all the Latin words for wheeled vehicles have a Celtic origin.

Along those high-speed roads, Greek merchandise had been flowing into Celtic lands since the sixth century BC. It was then that the port of Massalia (Marseille) was founded by traders from Phocaea. Soon, other Greek trading posts sprang up along the Mediterranean coast.

Massalia quickly became one of the most cosmopolitan cities in the ancient world. The traders and explorers who ventured up the Rhone and the Seine with trinkets and wine amphorae also brought intellectual treasures – surveying instruments and techniques, trigonometry and mathematics, Greek philosophy and science.

One of the commonest fallacies about the Celts is that they were illiterate. The only evidence for this is Caesar’s statement that the druids thought it sacrilegious to commit their teachings to writing. But he went on to say that: “In almost all other matters, public as well as private, they use the Greek alphabet.”

Caesar saw detailed population censuses written in Greek characters by Celtic scribes. Writing implements have been found all over the Celtic world, and a custom reported by Diodorus Siculus suggests that literacy rates were unusually high: “The Celts cast letters to their relatives onto funeral pyres in the belief that the dead will be able to read them.”

The druids themselves may have practised human sacrifice, but a religious ritual that now seems abhorrent is not necessarily a sign of savagery, especially in an age when Romans enjoyed the spectacle of bloody combat, and when their armies massacred or mutilated entire tribes. The druids were not the white-robed wizards of popular fiction, anachronistically depicted in the setting of a Stone Age temple. They were the intelligentsia of Celtic society. In fact, Caesar’s closest friend in Gaul was a druid called Diviciacus – a scientist, scholar and diplomat who once stayed at Cicero’s home on the Palatine Hill and addressed the Roman senate.

Diviciacus was a product of the most advanced education system in western Europe. A boy or a girl who went to druid school could expect to remain there for up to 20 years, which is as long as it takes today to go from nursery school to a doctoral degree. The curriculum included mathematics, natural and political science, history, law and religion. This meritocratic system was not reserved for the aristocracy: children of humble origins were able to attend druid school if their parents and relatives clubbed together to provide them with a scholarship.

Only fragments of the druids’ teachings have survived in Welsh and Irish legends, and yet much of their wisdom can be recovered. Five years ago, I discovered something that seemed at first impossible, and which I describe in my book The Ancient Paths: Discovering the Lost Map of Celtic Europe: the druids had not only organised their temples and towns using astronomical measure- ments, they had devised a continent-wide system of ‘solstice lines’ based on simple geometrical ratios. These solar paths had determined the orientation of roads, the location of settlements and battles, and the itineraries of tribal migrations. By applying the Greek system of latitude and longitude lines to Gaul and then, even more spectacularly, to Britain, the Celts created what is in effect the earliest accurate map of the world.

The same accuracy can be detected on a microcosmic level. The labyrinthine shapes of Celtic art seem to belong to a pre-classical world of swirling mists and superstition. Yet they, too, are governed by precise formulae. Even the humblest artefacts – a piece of harness or a fastening pin – are complex visual riddles. The strange faces that seem to peer out at us from Celtic designs are clues to a much greater pattern.

To the Romans, Celtic art was a closed book. Their prejudices, which have had such a corrosive effect on perceptions of our Celtic ancestors, were based on ignorance. Like most ridiculous ideas about foreigners, they were also born of fear. Long before Rome had an empire, Celtic tribes had colonised northern Italy. Milan, Turin and Bologna are all Celtic names. Rome itself was captured by an army of Celtic warriors in 387 BC. That humiliation was never forgotten. Centuries later, when the barbarians had been driven back over the Alps, the old fears still glowed like embers, and when Caesar brought civilisation to Gaul in the form of slavery and genocide, few voices in Rome were raised in protest.

It says a great deal about the vigour of Celtic culture that it survived the Roman invasion. Historians now talk about ‘the Roman interlude’, to stress the continuity of Celtic civilisation. Only a few generations after the Gallic War, tribal identities were stronger than ever, which is why so many French towns bear the original tribal name instead of the name imposed by the Romans: the Remi live in Reims, the Turones in Tours, and the Parisii still have a capital on the river Seine. In Britain, the Dark Age kingdoms retained the old Celtic boundaries, and some of the druids’ wisdom was preserved in early Christian rites and doctrine.

Perhaps the most pernicious Roman prejudice is the notion that the Celts were a race. Many people still believe that their Celtic heritage is inscribed in their DNA, in the colour of their hair or even in certain forms of behaviour. But it was precisely because the Celts were a culture, not an ethnic group, that their influence spread so rapidly to much of western Europe, even to parts of Ireland and Spain that were never invaded or settled by Celtic tribes. Everyone living in Europe today owes a great deal to the Celts, whether or not they have long hair, dress in tartan and drink undiluted wine.