Adelard of Bath would be in demand in the present day. This 12th-century English scholar, arrayed in his striped hat, brilliant green or red cape and lapis lazuli shirt, ‘had a talent’, Violet Moller explains, ‘for communicating complex scientific ideas and adapting them for an amateur, but interested, audience’. Yet he also devoted a good part of his time to profound research, translating mathematical, astronomical and astrological texts from Arabic – astrology being regarded in his time, especially at the Norman court in Sicily, as a very exact science with medical as well as political uses. Adelard knew that court well, but what is particularly interesting is that when he translated Euclid’s Elements into Latin he chose to do it not from its original Greek, the language of nearly half the population of Sicily at that time, but from Arabic, the language of the other half. Nor was he alone in taking such a route: works such as Ptolemy’s Almagest, fundamental for the medieval study of the heavens, seemed to inhabitants of Christian western Europe easier to understand through translation of the Arabic version rather than of the Greek original. The Arabic translators had interspersed their texts with explanations of terms and concepts the meanings of which in the original Greek puzzled western European readers, even if (as was rarely the case) they could understand that language.

Moller attempts to emulate Adelard’s haute vulgarisation. In the fashion of such works as Jerry Brotton’s A History of the World in Twelve Maps and Tristram Hunt’s Ten Cities That Made an Empire, she builds her narrative around a small number of documents and places with the aim of illustrating the way in which key classical texts were transmitted from antiquity through the Islamic world and on to medieval and Renaissance Europe. Her emphasis on the role of Arab science – or perhaps one should say Middle Eastern science, since Persian, Jewish and other non-Arab writers played a significant role too – mirrors the approach of popularisers such as Jim Al-Khalili in his book Pathfinders. Al-Khalili ably demonstrates the depth of scientific knowledge within the Islamic world at a time when European engagement with science was rather feeble, except in Muslim Spain. Moller tells a different but parallel story of the survival of Greek science in Arabic dress – a story of transmission, translation, text corruption and dissemination beginning in Baghdad and then leading to Córdoba, Toledo, Salerno, Palermo and Venice. Those are six of her seven cities. She builds her book around the legacy of three Greek authors whose works were of lasting importance, Euclid, Ptolemy and Galen, linking them to the seventh city, the great Hellenistic metropolis of Alexandria.

Moller is a lively guide, although like most guides she tends to exaggerate and often chooses the most exciting story rather than the most plausible one. For instance, her account of the career of the first emir of al-Andalus (Muslim Spain), Abd ar-Rahman I, who came to power in the mid-eighth century, follows the classic description of how he fled from the massacre of his dynasty, the Umayyads of Damascus, by their Abbasid rivals. After swimming through rivers and trailing across dusty deserts he ends up in the farthest corner of the Islamic world, Spain, where he raises the Umayyad flag once again. There may be a kernel of truth in all this, but the account we have comes from the 17th-century anthologist al-Maqqari, who lived in Algeria and often went for the best story.

Not just al-Maqqari but also historians writing in our own day have romanticised the history of medieval Spain, as Moller knows. By and large she steers a middle path between those who find evidence of harmonious convivencia (‘living together’) at every street corner and those who paint a much darker picture. She points to the rather neglected history of the Arabised Christians, or Mozarabs. The ninth century saw a wave of martyrdoms in Córdoba as Mozarabs stood up in public places to denounce Islam. Moller makes the excellent point that the Christians proved less well able to resist Islamisation than the Jews, who found it possible to attach themselves to the learning brought into Spain by the Arabs without seeing it as something that challenged their own beliefs. In the 12th century, the Mozarabs played an important role in translation work in Christian-ruled Toledo, but faced ecclesiastical disapproval of their rites. In consequence, all that survived of these by the early 16th century was the Mozarabic Mass, which is still somewhat monotonously recited in a chapel of Toledo Cathedral early each morning.

Moller livens up her already feisty narrative with a bit of fiction – not just that of al-Maqqari, but her own too. A quite superfluous passage depicts Abd ar-Rahman I lounging on colourful silk pillows in an anachronistically opulent garden of her imagination. Her template is the 14th-century Generalife in Granada, not the simpler al-Andalus of six centuries earlier. Moller’s imagination conjures up other fantasies too, such as sugar palm trees in Spain. The Jewish vizier of the great 10th-century ruler Abd ar-Rahman III, Hasdai ibn Shaprut, is dispatched by her as far as Frankfurt to meet the Holy Roman Emperor. In reality he stayed safely in Spain, where he offered sage advice to the monk John, an emissary of Otto I of Germany, who was overwhelmed by the showy magnificence of the Córdoban court. And her insistence that paper only began to be produced in Europe in the 14th century is contradicted by the vast amounts of paper documents in Italian archives from the century before. She seems unaware of the ‘paper revolution’ that took place in 13th-century Catalonia, leading to an explosion in record-keeping.

At times, Ptolemy, Galen and Euclid get lost in a wider account of the transmission of ideas, and they deserve more space. It would have been interesting, for example, to hear how Ptolemy was used in the age of Columbus, when scholars such as Abraham Zacuto, a Jew from Salamanca, produced astronomical tables drawing on the learning of the Greek and Arab worlds. These proved to be of great value to European explorers of the Atlantic and Indian Oceans. Of her three ancient authors, only Euclid was still being taught when I was at school – and just as well, because Ptolemy’s notion that the Indian Ocean was closed was disproved by Portuguese explorers around 1500, and his theory of an earth-centred universe was shown to be false by Copernicus, Brahe and Kepler in the century that followed. Nor, despite the apparent existence of a pharmacy called Galen Homeopathics in modern-day Dorset, would any of us place much trust in Galen’s elaborate theories about bodily humours and the nature of illness.

Some of Moller’s overambitious generalisations could have been avoided had she delved deeper into the literature, both primary and secondary. Judging from her notes and bibliography, she has often relied on quite superficial modern histories, which is surprising, as she has worked for the Bodleian Library, which possesses just about everything she would need to make this a deeper and more valuable book. That said, The Map of Knowledge offers a spirited account of crucial moments in the transmission of Greek learning through the Arab world to western Europe.