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D - 27: Algebra Reaches Pisa and then the World Beyond

Updated: Mar 26, 2021

1087 was a decisive year in the Mediterranean. Pirates were suddenly gone, the sea lanes to Egypt open again, Palestine was reachable within 10 sailing days, pilgrims and knights moved regularly between Italy and the Holy Land. The defeat of the Fatimid Fleet had opened a new chapter in history.

Old trade routes re-opened and the exchange of ideas resumed. Europeans learnt about the wonders of Damascus steel which could cut an iron sword into half, the Al-Nizamiyya Academy in Bagdad where law, algebra, literature and religious subjects were taught, the illustrated medical text books from the Baghdad Schools and of course of algebra which had reached the Middle East from India. Since the Seljuk Turks were the common enemy of both Arab and Christians, there was a certain level of cooperation despite the crusades. Even the lost classical Greek literature was accessible again. Translating Arab scripts into Latin was big business.

Making medicine from honey – School of Baghdad Medical Manuscript

There were few institutions of high learning in Europe yet. Bologna claims to have opened Europe’s first university in 1088 but it was a timid beginning. Institutions of High Learning were more prevalent in Muslim societies where they were built around palaces or mosques. The exchange and tradition of knowledge was not institutionalized yet. Copying and translating manuscripts was a time-consuming task and undertaken only by a few individuals who had the funds and time or the patronage for doing so.

“Liber Abaci” completed in 1202 with the Fibonacci sequence to the right

European medieval rulers were immensely interested in Arab knowledge. It was essential for the upgrading of their military capacity, to improve the tending of battle wounds, to manage taxes and improve navigation. It is thus no surprise that a power like Pisa took a keen interest in the world of science. It was directly applicable.

One of the people who gave Pisa access to this knowledge was Leonardo Bonacci di Pisa, commonly called Fibonacci (son of Bonacci). He was born in Pisa in 1170 where he also passed away 80 years later – a miraculously long life at the time. We know not too much about himself. He had an excellent reputation as a mathematician and entertained Emperor Frederick II., who loved math and science. But being a mathematician may not even have been his main job. He may have been first and foremost a merchant.

Leonardo Bonacci di Pisa 1170 – 1250 (can’t be a true picture since nobody made portraits in the 12th century)

Fibonacci’s father was a Pisan businessman in charge of a trading post in Algeria. He frequently brought his son along to his trips where young Bonacci got acquainted with the Arab way of calculating. Contrary to Europeans who still used Roman numbers, Arabs had switched to the Indian system and knew how to use zero. In his later years, Fibonacci travelled regularly to the Eastern Mediterranean – for business but also for studying. On his trips, he met merchants, officials and teachers who used the Arabic numerical system for book-keeping, exchanging money, converting weights (for coins), counting people or calculating profit or interest. Their place-value system made with 10 numbers only was much simpler to handle than the old Abacus.

When back in Pisa, Fibonacci worked on his field notes and consulted Arab sources to gain further insight. We have no proof but he must have been able to understand Arabic given the influence of several Arab mathematicians on his work. Over the years, he summarized his observations and by 1202 had completed a revolutionary book, his “Libri Abaci”. It was a ground -breaking publication, which contemporary mathematicians still refer to today. The book’s title “Libri Abaci” is actually misleading. It was not a book about the Abacus but the first European book about algebra. In his work, Fibonacci gave us composite fractions, factoring, arithmetic series and square pyramidal numbers, described irrational numbers (square roots) and a number series we call Fibonacci numbers today: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. whereby the first two numbers are added to produce the resulting number. Nature is organized with Fibonacci numbers. Not because nature is a mathematician but because cell division applying the golden rule is energy efficient. There are a few wonderful video clips on YouTube, which explain the phenomenon in simple language – it is fascinating. Encourage you to have a look.

The number of flower petals in nature follow the Fibonacci sequence

Whilst Fibonacci number sequences are fascinating, the real revolution Leonardo di Pisa triggered was the use of algebra in Europe. Without it, double entry accounting would not have been invented, precise scientific observations and measurements would never be possible, books on math could not be written – math in itself would not have progressed.

All this happened at Pisa, one of the most powerful city states in Europe ever. Pisa was not only rich, it also had a rich network of connections to draw from. It was literally a sponge that absorbed anything that was useful. The town understood that early mastery of technology has tangible benefits, be it money or power. At the end of his long career and service, the Republic honored Fibonacci for his contributions with a life-long endowment.

Whether Fibonacci tried his hand on the problem of Pisa’s leaning tower - it started tilting from the very beginning – is unknown. It would not surprise me.

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