The works of great Indian mathematicians Aryabhata and Brahmagupta and the highly efficient Indian numeral system were introduced to Baghdad, the capital of the Abbāsid Caliphate, in the eighth century, marking a cross-civilisational knowledge exchange that shaped modern mathematics
Barmakids were a family from Balkh in what is now northern Afghanistan. They gained prominence in the eighth century as scribes and viziers to the Abbāsid Caliphate, which oversaw the peak of the Islamic Golden Age likened to Italy’s High Renaissance. Barmakids were originally Buddhist abbots who mastered Indian mathematics. Khalid ibn Barmak (709-781/82, who established the Barmakid family at the top of the caliphate, studied in Kashmir, then a center of philosophy and advanced mathematics.
The Barmakids brought the works of great Indian mathematicians Aryabhata and Brahmagupta, and the highly efficient Indian numeral system to Baghdad, the capital of the Abbāsid Caliphate, marking the start of a knowledge exchange across civilizations that shaped modern mathematics. The system of nine numerals and zero made multiplication and division simpler. It helped develop the decimal system and calculus, which are vital to almost all branches of science and underpin important discoveries in physics.
Scholars such as ninth-century polymath Muhammad ibn Musa Al-Khwarizmi (780–850), who gave algorithms his name, built on Indian ideas to create what is known as the Arab hegemony in mathematics. The numeral system, which Europeans call Arab numerals and the Arabs correctly describe as Hindsa or the Indian numeral, reached Renaissance Europe centuries after Aryabhata’s extraordinary contributions to astronomy and mathematics.
Baghdad’s House of Wisdom and Indian Mathematics
Brahmagupta developed Aryabhata’s ideas. He took the concept of zero, which had existed in Babylon (modern-day Iraq) and Egypt in earlier forms, and treated it as a number with its own mathematical properties. The Babylonians and Egyptians used zero-like symbols as placeholders or indicators of absence. Brahmagupta recognised zero as a number that could be manipulated mathematically. He defined zero as the result of subtracting a number from itself. He showed that adding or subtracting zero leaves a number unchanged. Multiplying a number by zero yields zero.
Brahmagupta gave arithmetical rules in terms of fortunes (positive numbers) and debts (negative numbers). He opened the way for advances in place value, calculations involving tens, hundreds, thousands, and beyond, and the development of higher mathematics. In Baghdad, Brahmagupta’s works were translated into Arabic at the iconic academy, Bayt al-Hikmah, believed to have been as big as the present-day British Library, the world’s largest with up to 200 million catalogued items, and Paris’s Bibliothèque Nationale.
Multi-religious and multi-ethnic scholars studied mathematics, astronomy, medicine, geography, philosophy, and literature at Bayt al-Hikmah (House of Wisdom). The academy was a site of scientific innovation and a repository of ancient Egyptian, Mesopotamian, Persian, Greek, Indian, and Chinese works translated into Arabic. Algebra, trigonometry, and chemistry emerged as new disciplines there. Bayt al-Hikmah helped major advances in medicine, astronomy, engineering, and agriculture. Arabic texts replaced Greek as the fount of wisdom and helped shape Renaissance science. The 1001 Inventions exhibition at London’s Science Museum showcases some of this era’s achievements.
Zero to Algorithms: How Indian and Muslim Scholars Transformed Mathematics
Bayt al-Hikma helped spread transformative concepts like zero. The first written record of a zero appeared in ancient Mesopotamia and denoted nothingness. Indian mathematicians gave meaning to zero in the fifth century. The idea spread to the Arab world, although the Mayans are thought to have been using zero centuries earlier. Bayt al-Hikmah ushered in a cultural Renaissance that altered the course of mathematics, introducing abstract mathematical language that was adopted globally.
Al-Khwarizmi, who came to Baghdad from Khwarazm in what is now Uzbekistan, was a major figure of this era. Khwarizmi combined Aryabhata and Brahmagupta’s insights with Greek mathematical ideas and other intellectual traditions. He wrote a book titled al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābalah (The Compendious Book on Calculation by Completion and Balancing). The word algebra comes from the Arabic word al-jabr in the book’s title.
Algorithms, now critical to our daily lives, would not have been possible without Al-Khwarizmi. The term algorithm comes from the Latinized version of Al-Khwarizmi’s name, Algorismus. Khwarizmi headed the storied Bayt al-Hikmah. His work is considered the foundational text of modern algebra. Khwarizmi presented a systematic way of solving quadratic equations for the first time. His approach to mathematics made much of modern algorithmically-based technology possible. Science historian George Sarton has called the period between 800-850 CE ‘the Time of al-Khwārizmi’.
Indian-Arab Numerals, Fibonacci and Transformation of European Mathematics
Fundamental mathematical terms emerged from the meeting of Indian and Arabic scholarship in ninth-century Baghdad. The system spread rapidly throughout the Islamic world, which then extended to Spain. It reached Christian monks at the monastery of Ripoll, near Barcelona. Europe clung to Roman numerals until the 12th century, when Italian mathematician Leonardo da Pisa, known posthumously as Fibonacci, transmitted the ‘Arabic (Indian) numeric system’ to Europe and made him synonymous with mathematics there.
Fibonacci was educated in what is now Algeria, where Fibonacci’s father ran an Italian trading establishment in the town of Béjaia. When Fibonacci returned to Italy, he found his contemporaries were struggling with Roman numerals. He wrote Liber Abaci, or The Book of Calculation, bringing the numeral system from North Africa to Italy, where it spread.
Liber Abaci relied almost wholly on Khwarizmi’s algorithms for using numerals to calculate profit margins, money changing, weight conversion, barter, and interest. Fibonacci wrote that those wishing to know the art of calculating, its subtleties and ingenuities, ‘must know computing with hand figures, or nine figures and zero.’
Muslim Mathematical Innovations and the European Renaissance
The Holy Roman Emperor Frederick II got interested in this more efficient approach to mathematics. The approach became foundational to Renaissance mathematical learning. Piero della Francesca, one of the great Renaissance painters, wrote three treatises, incorporating these mathematical ideas, including those related to perspective, in Florence. Francesca’s work influenced scholars in Milan.
In December 2020, Adrienne Bernhard wrote on bbc.com that Fibonacci’s great genius was his keen understanding of the advantages Muslim scientists knew for centuries: their calculating formulas, their decimal place system, their algebra. She argued Fibonacci’s ‘transformative influence on modern maths was thus a legacy owed in great part to Al-Khwarizmi’, the father of algebra. She underlined that Fibonacci’s most enduring mathematical contribution is something rarely taught in schools.
The story began at Bayt al-Hikma nearly a thousand years ago when most of Western Christendom lay in intellectual darkness. Bernhard wrote that it should dismantle the Eurocentric view of mathematics, spotlight the Islamic world’s scientific achievements, and argue for the continued importance of numerical treasures from long ago.
