Greece played a crucial role in the transmission of classical knowledge to the Islamic world. Its rich historiographical tradition preserved Ancient Greek knowledge upon which Islamic art, architecture, literature, philosophy and technological achievements were built. Ibn Khaldun once noted; The sciences of only one nation, the Greeks, have come down to us, because they were translated through Al-Ma'mun’s efforts. He was successful in this direction because he had many translators at his disposal and spent much money in this connection.

Scholar Toby Huff lists twelve major intellectuals from Greece that immensely influenced Islamic scholars, and notes the extraordinary impact that Greek natural science and philosophy had on the Islamic Golden Age, stating that: One example of Greek influence is in the field of Islamic medicine, in which Islamic medicine was primarily founded upon the legacies of Greek and Roman physicians and scholars, most notably Galen and Hippocrates. Islamic scholars carefully translated these extensive medical works from Greek into Arabic, using them as the foundation to subsequently generate new medical knowledge. The common and persistent myth claiming that Islamic scholars “saved” the classical work of Aristotle and other Greek philosophers from destruction is inaccurate. Arabic scholars were indeed responsible for the initial transmission of many Greek texts to Western Europe (translated to Latin from Arabic), with many original Greek texts not leaving the Byzantine Empire until the Renaissance. Medieval possession of Greek texts in Latin was largely thanks to Arabic scholars, but today the original Greek is accessible thanks to Renaissance scholars. According to the myth, these works would otherwise have perished in the long European Dark Ages between the fifth and the tenth centuries. Ancient Greek texts and Greek culture were never “lost” to be somehow “recovered” and “transmitted” by Islamic scholars, but rather were preserved and studied by the scholars and monks of the Byzantines and passed on to the rest of Europe and to the Islamic world at various times. Aristotle had been translated in France at the abbey of Mont Saint-Michel before translations of Aristotle into Arabic (via the Syriac of the Christian scholars from the conquered lands of the Byzantine Empire). Michael Harris points out:

Historian John Julius Norwich adds that “much of what we know about antiquity—especially Hellenic and Roman literature and Roman law—would have been lost forever if it weren’t for the scholars and scribes of Constantinople.”

Ibn Khaldun pointed out that the one civilization from which the Arabs had learned the sciences, was that of the Greeks, thanks to the translations by Christian (Assyrians) scholars of Greek texts into Syriac and then into Arabic. Ibn Khaldun also records that Abbasid caliph al-Mansur requested from the Byzantine Emperor the mathematical works of the Greeks.

Hellenistic period The Hellenistic period began in the 4th century BC with Alexander the Great's conquest of the eastern Mediterranean, Egypt, Mesopotamia, the Iranian plateau, Central Asia, and parts of India, leading to the spread of the Greek language and culture across these areas. Greek became the language of scholarship throughout the Hellenistic world, and Greek mathematics merged with Egyptian and Babylonian mathematics to give rise to a Hellenistic mathematics.

The most important centre of learning during this period was Alexandria in Egypt, which attracted scholars from across the Hellenistic world, mostly Greek and Egyptian, but also Jewish, Persian, Phoenician scholars.George G. Joseph (2000). The Crest of the Peacock, p. 7-8. Princeton University Press. .

Most of the mathematical texts written in Greek have been found in Greece, Egypt, Asia Minor, Mesopotamia, and Sicily.

Classical and ecclesiastical studies Byzantine science was essentially classical science. Therefore, Byzantine science was in every period closely connected with ancient-pagan philosophy, and metaphysics. Despite some opposition to pagan learning, many of the most distinguished classical scholars held high office in the Church. The most noteworthy oppositions include the closing of the Platonic Academy in 529, the obscurantism of Cosmas Indicopleustes, the condemnation of Ioannis Italos (1082) and of Georgios Plethon because of their devotion to ancient philosophy. The writings of antiquity never ceased to be cultivated in the Byzantine Empire due to the impetus given to classical studies by the Academy of Athens in the 4th and 5th centuries, the vigor of the philosophical academy of Alexandria, and to the services of the University of Constantinople, which concerned itself entirely with secular subjects, to the exclusion of theology,The faculty was composed exclusively of philosophers, scientists, rhetoricians, and philologists () which was taught in the Patriarchical Academy. Even the latter offered instruction in the ancient classics, and included literary, philosophical, and scientific texts in its curriculum. The monastic schools concentrated upon the Bible, theology, and liturgy. Therefore, the monastic scriptoria expended most of their efforts upon the transcription of ecclesiastical manuscripts, while ancient-pagan literature was transcribed, summarized, excerpted, and annotated by laymen or enlightened bishops like Photios, Arethas of Caesarea, Eustathius of Thessalonica, and Basilius Bessarion.

When Saint Cyril was sent by the Byzantine emperor in an embassy to the Arabs in the ninth century, he astonished his Muslim hosts with his knowledge of philosophy and science as well as theology. Historian Maria Mavroudi recounts:

Mathematics Byzantine scientists preserved and continued the legacy of the great Ancient Greek mathematicians and put mathematics in practice. In early Byzantium (5th to 7th centuries) the architects and mathematicians Isidore of Miletus and Anthemius of Tralles used complex mathematical formulas to construct the great Hagia Sophia church, a technological breakthrough for its time and for centuries afterwards due to its striking geometry, bold design and height. In late Byzantium (9th to 12th centuries) mathematicians like Michael Psellos considered mathematics as a way to interpret the world.

After learning of Leo the Mathematician, the Abbasid caliph al-Mamun was so impressed by his knowledge of mathematics, providing proofs that his own scholars were unable to complete, and predictive abilities that he offered Leo great riches to come to Baghdad.According to Joseph Genesius and Theophanes Continuatus between 829 and 833; Symeon the Logothete makes the caliph al-Mutasim and puts the invitation after the Islamic conquest of Amorium in the fall of 838, cf.

Medicine

Medicine was one of the sciences in which the Byzantines improved on their Greco-Roman predecessors. As a result, Byzantine medicine had an influence on Islamic medicine as well as the medicine of the Renaissance.

The first known Greek medical school opened in Cnidus in 700 BC. Alcmaeon, author of the first anatomical work, worked at this school, and it was here that the practice of observing patients was established. Ancient Greek medicine revolved around the theory of humours. The most important figure in ancient Greek medicine is the physician Hippocrates, known as the "Father of Medicine", who established his own medical school at Cos.Atlas of Anatomy, ed. Giunti Editorial Group, Taj Books LTD 2002, p. 9 Hippocrates and his students documented many conditions in the Hippocratic Corpus, and developed the Hippocratic Oath for physicians, still in use today. The Greek Galen was one of the greatest surgeons of the ancient world and performed many audacious operations—including brain and eye surgeries— that were not tried again for almost two millennia. The writings of Hippocrates, Galen, and others had a lasting influence on Islamic medicine and Medieval European medicine until many of their finding eventually became obsolete from the 14th century onwards.

Unani Medicine (; Yūnānī in Arabic, Hindustani and Persian), also spelled Yunani Medicine, means "Greek Medicine", and is a form of traditional medicine widely practiced in South Asia. It refers to a tradition of Graeco-Arabic medicine,Unani Medicine in India: Its Origin and Fundamental Concepts by Hakim Syed Zillur Rahman, History of Science, Philosophy and Culture in Indian Civilization, Vol. IV Part 2 (Medicine and Life Sciences in India), Ed. B. V. Subbarayappa, Centre for Studies in Civilizations, Project of History of Indian Science, Philosophy and Culture, New Delhi, 2001, pp. 298-325 which is based on the teachings of Greek physician Hippocrates, and Roman physician Galen, and developed into an elaborate medical System by Arab and Persian physicians, such as Rhazes, Avicenna (Ibn Sena), Al-Zahrawi, Ibn Nafis.

An author observed that “The fourth Umayyad Caliph, Marwan I, ordered the translation … of the famous medical treatise of Aaron of Alexandria. The translation of medical literature was in fact a principal aspect of the scientific progress that distinguished the rule of the Umayyads.”

The oldest scientific work in Arabic was a discourse on medicine, which was written by Aaron of Alexandria, a Greek Christian priest, and translated from the Syriac language then into Arabic in the year 683 by a Jewish doctor from Basra named Masarjawaih.

Immense scientific knowledge, (such as Galenic medical knowledge), fell into the hands of Muslims after their military conquest of the Christian city of Alexandria in the year 642. Muslim physicians would build upon these Greek works for their later reputation in the medical field.

Greek fire

Greek fire was an incendiary weapon used by the Byzantine Empire. The Byzantines typically used it in naval battles to great effect as it could continue burning even on water. It provided a technological advantage, and was responsible for many key Byzantine military victories, most notably the salvation of Constantinople from two Arab sieges, thus securing the Empire's survival. Greek fire proper however was invented in c. 672, and is ascribed by the chronicler Theophanes to Kalliniko, an architect from Heliopolis in the former province of Phoenice, by then overrun by the Muslim conquests.

Byzantine architecture

Byzantine Greek architecture in the West gave way to Romanesque and Gothic architecture. In the East it exerted a profound influence on early Islamic architecture, During the Umayyad Caliphate era (661-750), as far as the Greek impact on early Islamic architecture is concerned, the Greek artistic heritage formed a fundamental source to the new Islamic art, especially in Syria and Palestine. There are considerable Byzantine influences which can be detected in the distinctive early Islamic monuments in Syria and Palestine, as on the Dome of the Rock (691) at Jerusalem, the Umayyad Mosque (709-15) at Damascus. While the Dome of the Rock gives clear reference in plan - and partially in decoration - to Byzantine art, the plan of the Umayyad Mosque has also a remarkable similarity with the 6th- and 7th-century Christian basilicas, but it has been modified and expanded on the transversal axis and not on the normal longitudinal axis as in the Christian basilicas. This modification serves better the liturgy for the Islamic prayer. The original mihrab of the mosque is located almost in the middle of the eastern part of the qibla wall and not in its middle, a feature which can be explained by the fact that the architect might have tried to avoid the impression of a Christian apse which would result from the placement of the mihrab in the middle of the transept. The tile work, geometric patterns, multiple arches, domes, and polychrome brick and stone work that characterize Islamic and Moorish architecture were influenced by Byzantine architecture.