How a prestigious Islamic library brought modern mathematics to the world!
A famous Islamic library centuries ago introduced Arabic numerals to the world. Though the library has long since disappeared, our society has changed through its mathematical revolution.
T
he House of Wisdom sounds a little like a belief: there is no trace left of this ancient library that was demolished in the 13th century, so we can’t be sure exactly where it was or what it looked like.
But during the Islamic Golden Age, this prestigious academy was actually a major intellectual powerhouse in Baghdad, and the birthplace of mathematical principles as transformative as the traditional zero and our modern ”Arabic” numerals.
Established in the late 8th century as a private collection for Caliph Harun Al-Rashid, then transformed into a public academy some 30 years later, the House of Wisdom seems to have attracted scientists from around the world to Baghdad, drawn as they were by the vibrant intellectual curiosity and freedom of expression of the region (Muslim, Jewish and Christian scholars were all allowed to study there).
The House of Wisdom gradually became an unrivalled centre for the study of humanities and sciences, including mathematics, astronomy, medicine, chemistry, geography, philosophy, literature and the arts, as well as some more questionable subjects such as alchemy and astrology, an archive as formidable in scale as the new British Library in London or the Bibliothèque Nationale of Paris.
It therefore takes a leap of imagination to conjure this great monument (think the Citadel in Westeros, or the library at Hogwarts), but one thing is certain the academy ushered in a cultural Revival that would fully alter the course of mathematics.
In the Mongol Siege of Baghdad in 1258, the House of Wisdom was destroyed (according to legend, so many manuscripts were tossed into the Tigris River that its waters turned black from ink), but the discoveries made a strong, abstract mathematical language introduced there that would later be embraced by the Islamic empire, Europe, and eventually the whole world.
“It’s not the precise details of where or when the House of Wisdom was created that should matter to us,” says Jim Al-Khalili, a physics professor at the University of Surrey. “The history of scientific ideas themselves, and how they have developed as a result, is far more interesting.”
Tracing the mathematical legacy of the House of Wisdom requires a bit of time travelling, as it were, back to the future. One name was associated with mathematics in Europe for hundreds of years before the height of the Italian Renaissance: Leonardo da Pisa, known posthumously as Fibonacci. The Italian mathematician, born in Pisa in 1170, received his main training in Bugia, a trading enclave on the African coast of Barbary (coastal North Africa). Fibonacci moved to the Middle East in his early 20s, captivated by ideas that had come from India via Persia to the west. Fibonacci wrote Liber Abbaci, one of the first Western works to describe the Hindu-Arabic numerical method, when he returned to Italy.
When Liber Abbaci first appeared in 1202, only a few intellectuals knew Hindu-Arabic numerals; European tradesmen and scholars mostly clung to Roman numerals, making multiplication and division extremely cumbersome (try to multiply MXCI by LVII!). Fibonacci’s book showed the use of numerals in arithmetic operations, techniques that could be applied to practical issues such as profit margin, change of capital, conversion of weight, barter and interest.
In the first chapter of his encyclopedic work, Fibonacci wrote, “Those who want to know the art of calculating, its subtleties and ingenuities, must know computing with hand figures,” referring to the digits that children now study in school. “Any number whatsoever is written with these nine figures and the sign 0, called zephyr.” Unexpectedly, in a useable form, mathematics was open to everyone.
The great genius of Fibonacci, however was not just his ingenuity as a mathematician, but his keen knowledge of the benefits that Muslim scientists have known for centuries: their measuring formulas, their decimal place method, their algebra. Liber Abbaci, in fact, relied almost entirely on the 9th-century mathematician Al-Khwarizmi. For the first time, his revolutionary treatise introduced a systematic way of solving quadratic equations. Al-Khwarizmi is sometimes referred to as the father of algebra because of his discoveries in the field, a term we owe to him from the Arabic al-jabr, “the restoration of broken parts,” and he was named astronomer and head librarian of the House of Wisdom in 821.
The treatise of Al-Khwarizmi opened the Muslim world to the system of decimal numbers,” Al-Khalili explains. “Others such as Leonardo da Pisa, have contributed to its transmission across Europe.”
The transformative influence of Fibonacci on modern mathematics was thus a legacy owed in large part to Al-Khwarizmi. And so the ancient library connected two men separated by almost four centuries: the most famous mathematician of the Middle Ages stood on the shoulder of another pioneering thinker, one whose breakthroughs had been made in an iconic institution of the Islamic Golden Age.
Perhaps because so little is known about the House of Wisdom, historians are occasionally tempted to exaggerate its scope and purpose, giving it a mythic status somewhat at odds with the scant historical records left to us. ” Some argue that in the eyes of many, the House of Wisdom was nothing as grand as it had become,” Al-Khalili says. “But its association with men such as Al-Khwarizmi, with his work in mathematics, astronomy and geography, is for me strong evidence that the House of Wisdom was closer to a true academy, not just a repository of translated books.”
In order to ensure that their work was available to the reading public, scholars and translators at the library also took great pains. “The House of Wisdom is fundamentally important because we formed the foundation of our mathematical understanding through translations there-Arabic scholars who translated Greek ideas into vernacular-” says June Barrow-Green, professor of mathematics history at the Open University in the United Kingdom. The palace library was as much a window into numerical ideas from the past as it was a site of scientific innovation.
Long before our current decimal system, the binary number system that program our computers, human beings used early tally systems to record calculations, before Roman numerals, before the system used by ancient Mesopotamians. While we may find each of these unprecedented or antiquated, different numerical representations can actually teach us something useful about the structure, relationships, and historical and cultural contexts from which they originated.
The concept of place value and abstraction is reinforced, helping us to better understand how numbers work. They show that “not the only way was the Western way,” says Barrow-Green. “There is a real value in understanding various systems of numbers.”
For instance, when an ancient trader wanted to write “two sheep” she could inscribe a picture of two sheep in clay. But if she were to write “20 sheep,” this would be unrealistic. Sign-value notation is a scheme in which adding numeric symbols together signifies a value; in this case, drawing two sheep to indicate the actual amount.
A vestige of sign-value notation, despite the introduction of Al-scheme, Khwarizmi’s which relied on the location of digits to denote quantities, Roman numerals somehow persisted. Roman numerals outlived the empire that gave birth to them like the towering monuments on which they were engraved, whether by accident, emotion or intention, none can say for sure.
This year marks the 850th anniversary of Fibonacci’s birth. It could also be the moment which threatens to undo the journeywork of Roman numerals. In the UK, traditional time-pieces have been replaced with easier-to-read digital clocks in school classrooms,for fear students can no longer tell analogue time properly. In some regions of the world, governments have dropped them from road signs and official documents, while Hollywood has moved away from using Roman numerals in sequel titles. The Superbowl famously ditched them for its 50th game, worried it was confusing fans.
But a global shift away from Roman numerals underscoresa creeping innumeracy in other aspects of life. Perhaps more important, the disappearance of Roman numerals reveals the politics that govern any wider discussion about mathematics.
Many of us will find nothing special about the figure MMXX (that’s 2020, if you’re unaware). We may dimly recognise Fibonacci for the famous pattern named after him: a recursive sequence that starts with 1 and is thereafter the sum of the two previous numbers.
The Fibonacci sequence is certainly remarkable, showing up with astonishing frequency in the natural world – in seashells and plant tendrils, in the spirals of sunflower heads, in pine cones, animal horns and the arrangement of leaf buds on a stem, as well as the digital realm (in computer science and sequencing). His patterns often make their way into popular culture, too: in literature, film and visual arts; as a refrain in song lyrics or orchestral scores; even in architecture.
But Leonardo da Pisa’s most enduring mathematical contribution is something rarely taught in schools. That story begins in a palace library nearly a thousand years ago, at a time when most of Western Christendom lay in intellectual darkness. It is a tale that should dismantle our Eurocentric view of mathematics, shine a spotlight on the Islamic world’s scientific achievements and argue for the continued importance of numerical treasures from long ago.
