Fibonacci: Ten Symbols {0,1,2,3,4,5,6,7,8,9}

Following up on last week’s post, “Pythagoras of Samos: From Earth to the Sphere of the Moon, One Tone” today’s LinkedIn newsletter features Leonardo of Pisa, known almost exclusively under his byname Fibonacci, which immediately awakens association with the Fibonacci sequence named after him.

When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms.

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Before the 13th century Europeans used Roman numerals to do arithmetic. Fibonacci is largely responsible for reintroducing what’s considered the Hindu–Arabic number system in the west, which revolutionized not only mathematics but commerce and trade as well. Simple marking by scratches or dots, one for each item being counted, was the norm long into human history.

Early traders recorded their numerical data using Roman numerals and performed calculations either by a widely used fingers procedure or with an abacus.

One of the earliest proofs of math skills practice is a papyrus written by an Egyptian scribe named Ahmes (1650 B.C.), who recorded a series of 87 exercises and problems.

Coming into contact with the mathematical knowledge of various cultures on his journeys, Fibonacci combined the knowledge he acquired with his own thinking and committed the entire store of knowledge to paper on his return home.

Little is known about his life except that he was the son of a customs official. As a child, Fibonacci travelled around North Africa with his father, Guilielmo, who ran a Pisan trading post in Bugia in present-day Algeria. There where he learned about Arabic mathematics from an Islamic teacher.

On his return to Italy, he helped to disseminate this knowledge throughout Europe, thus setting in motion a rejuvenation in European mathematics, which had lain largely dormant for centuries during the Dark Ages.

Despite its obvious advantages, uptake of the system in Europe was slow (this was after the time of the Crusades against Islam), and Arabic numerals were even banned in the city of Florence in 1299 on the pretext that they were easier to falsify than Roman numerals. However, the new system was adopted throughout Europe by the 15th century, making the Roman system obsolete.

Traveling around the Mediterranean coast, Fibonacci met with many merchants, learning about their systems of doing arithmetic. He soon realized the many advantages of the Hindu-Arabic system, which, unlike the Roman numerals used at the time, allowed easy calculation using a place-value system composed of the ten symbols {0,1,2,3,4,5,6,7,8,9}. The book showcased the practical use and value of this by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, and other applications.

Around 1200, Fibonacci returned to Pisa where he lived as a private scholar and mathematical writer. In 1202, "Liber abaci" whose title translates as the Book of Calculation, was completed. The book disclosed arithmetic methods to the Western world on the basis of terms that ordinary people could understand — tradesmen and businessmen as well as schoolchildren.

Fibonacci's second work is entitled the Practica geometriae, and draws heavily on the works of the ancient Greek mathematicians, including Euclid and Archimedes.

Roman emperor, Frederick II, became aware of Fibonacci's work through the scholars at his court who had corresponded with him since his return to Pisa around 1200. Johannes of Palermo, a member of Frederick II's court, presented a number of problems as challenges to Fibonacci. Three of these problems were solved by Fibonacci and he gives solutions to them in Flos (1225) which he sent to Frederick II.

Fibonacci’s real significance resides not in the discovery of the Fibonacci sequence, but in the fact that studying ancient science and encountering Arab mathematics led him to produce a number of writings that laid the foundation for applied mathematics in the west.

It is assumed that he was born around 1170 and died after 1240, probably in Pisa.

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About the Author: Lawrence Jean-Louis is the founder of eBrand Me, a digital marketing agency offering marketing & consultative services to CPAs and tax professionals. She aspires to start a money management firm by 2030.