When Iran was taken during the Arab Conquest the Persians were resistant to the new rulers of their land. The Arabs found an empire rich and well developed during the golden era of the Sasanid Dynasty and thus the Persians attempted to retain as much of that as they could. For starters, they resisted converting to Islam as most of them were Zoroastrian (a religion practiced in Iran from 1700BCE) and it was only during the Middle Ages that most of the conversions took place. They also resisted Arabic as their lingua franca but compromised by translating the Arabic alphabet into Persian and adding four more letters to the alphabet to accommodate their language.
There is an old saying in Iran: "Instead of Persians becoming influenced by invaders, they Persianize the invaders" and that is exactly what happened. The Persian arts was the single most influential force in Islamic arts as we know it today. A key form of Islamic art that is world renowned is calligraphy. This is an art form that they learned from the Persians who have already developed it during Achaemenid times 500BC. The Persian miniatures (done before the Sasanid Empire) were also incorporated into Islamic texts and paintings. Persian metalwork, carpets, silk, glass work, ceramics, tiles, poetry and architecture were all used and adapted by the various different Islamic empires that ruled Persia.
Persian architectural designs that were used and modified were paradise garden, courtyards, hypostyle halls, arches, vaulting, squinches, muqarnas, iwans and pishtaqs. Islamic geometric patterns, such as the girih tiles, were also derived from Greek, Roman and Sasanid influences, with many great examples in mosques and buildings in Iran.
The intellectual tradition in Persia continued after Islam and was of great influence on the further development of Iranian Philosophy. In the Islamic Golden Age, due to Avicenna's successful reconciliation between Aristotelianism and Neoplatonism along with Kalam, Avicennism eventually became the leading school of Islamic philosophy by the 12th century. Avicennism was also influential in medieval Europe, particularly his doctrines on the nature of the soul and his existence-essence distinction, along with the debates and censure that they raised in scholastic Europe.
Rumi, one of Iran's foremost philosophers, was also active during the Islamic Golden Age. Rumi's poetry forms the basis of much classical Iranian and Afghan music. To many modern Westerners, his teachings are one of the best introductions to the philosophy and practice of Sufism. Today Rumi's poems can be heard in churches, synagogues, Zen monasteries, as well as in the downtown New York art/performance/music scene.
Another Persian philospher is Al-Khwarizmi, His popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm.
Omar Khayyam was another Persian mathematician, astronomer and poet active during the Islamic Golden Age. As a mathematician, he is most notable for his work on the classification and solution of cubic equations, where he provided geometric solutions by the intersection of conics. Khayyam also contributed to the understanding of the parallel axiom. As an astronomer, he designed the Jalali calendar, a solar calendar with a very precise 33-year intercalation cycle.
There is a tradition of attributing poetry to Omar Khayyam, written in the form of quatrains.This poetry became widely known to the English-reading world in a translation by Edward FitzGerald (Rubaiyat of Omar Khayyam, 1859), which enjoyed great success in the Orientalism of the fin de siècle.
Hafez was a Persian poet during the 14th century who "lauded the joys of love and wine but also targeted religious hypocrisy". His collected works are regarded as a pinnacle of Persian literature and are often found in the homes of people in the Persian-speaking world, who learn his poems by heart and still use them as proverbs and sayings. Hafez is best known for his poems that can be described as "antinomian" and with the medieval use of the term "theosophical"; the term "theosophy" in the 13th and 14th centuries was used to indicate mystical work by "authors only inspired by the holy books" (as distinguished from theology). Hafez primarily wrote in the literary genre of lyric poetry, or ghazals, that is the ideal style for expressing the ecstasy of divine inspiration in the mystical form of love poems. His influence on Persian speakers appears in "Hafez readings" and in the frequent use of his poems in Persian traditional music, visual art, and Persian calligraphy. Adaptations, imitations and translations of his poems exist in all major languages.
Al-Biruni is regarded as one of the greatest scholars of the medieval Islamic era and was well versed in physics, mathematics, astronomy, and natural sciences, and also distinguished himself as a historian, chronologist and linguist. He studied almost all fields of science and was compensated for his research and strenuous work. Royalty and powerful members of society sought out Al-Biruni to conduct research and study to uncover certain findings. He lived during the Islamic Golden Age, in which scholarly thought went hand in hand with the thinking and methodology of the Islamic religion. In addition to this type of influence, he was conversant in Khwarezmian, Persian, Arabic, Sanskrit, and also knew Greek, Hebrew and Syriac. In 1017 he travelled to South Asia and authored a study of Indian culture (Tahqiq ma li-l-hind...) after exploring the Hinduism practised in India. He was given the title "founder of Indology". He was an impartial writer on customs and creeds of various nations, and was given the title al-Ustadh ("The Master") for his remarkable description of early 11th-century India.
Ferdowsi was a Persian poet during the Islamic Golden Era and the author of Shahnameh ("Book of Kings"), which is the world's longest epic poem created by a single poet, and the national epic of Greater Iran. Ferdowsi is celebrated as the most influential figure in Persian literature and one of the greatest in the history of literature.