Ninth-century Baghdad was the scientific capital of the world. The Abbasid caliphs Harun al-Rashid and his son al-Ma'mun founded a vast academic centre that translated manuscripts from Byzantium, Alexandria, and India into Arabic: Bayt al-Hikma — the House of Wisdom. Mathematicians, astronomers, philosophers, physicians, and translators worked together. Al-Ma'mun's observatories measured the circumference of the Earth with remarkable accuracy; the translators brought Aristotle, Euclid, Galen, and Indian mathematical texts into Arabic.

The emblematic figure of this milieu is Muhammad ibn Musa al-Khwarizmi (c. 780–850). Around 820 he wrote Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala, the first comprehensive systematic treatise on solving equations. "Al-jabr" is Arabic for "completion/restoration"; when the word entered European usage it became "algebra". Al-Khwarizmi's Latinised name, "Algoritmi", became "algorithm" in European languages — today the underlying concept of every computer program.

Al-Khwarizmi also brought the Indian decimal numeral system (the digits 0–9 and zero) into the Arab world; from there it spread to Europe. Anyone who has tried doing arithmetic in Roman numerals understands what this system gave to commerce, accounting, and science: a universal language. He also wrote on astronomical tables, maps, and calendar calculations.

The library of the House of Wisdom was destroyed in 1258 when the Mongols sacked Baghdad — the famous image is of the Tigris running black with ink for days. But the knowledge that had reached al-Andalus from Baghdad was, from there, translated into Latin Europe; it is one of the foundations of the Renaissance. When today we speak of the "Islamic Golden Age", the House of Wisdom and al-Khwarizmi sit at its centre.