Fibonacci’s Intellectual Legacy

This is an excerpt from Master Fibonacci: The Man Who Changed Math. All citations are catalogued on the Citations page.

LEONARDO PISANO’S DEATH AND MEMORIAL

(Previous Section: Liber Abaci)

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No one knows when or how Leonardo of Pisa died (Horadam). After publication of his revised version of Liber Abaci in 1228, only one known document refers to him. This is a decree made by the Republic of Pisa in 1241 in which “the serious and learned Master Leonardo Bigollo” was granted an annual honorarium of twenty Pisan pounds plus expenses for services to the city. Historians believe this was either in return for advising on matters of accounting (such as advising on financial contracts stipulating long-term debt commitments to creditors) and teaching the citizens, or for service as city auditor (O’Connor and Robertson; Devlin, Man 99).

Even though he was famous in his lifetime as a brilliant mathematics expositor and, later, as a respected public servant, Leonardo was forgotten within 200 years of his death. Devlin says this should not be surprising since, “other than nobility, few people had anything recorded about them, even those who had achieved great things” (Finding 22). His name did not appear in any book on the history of science or mathematics for 400 years.

In 1495, Luca Paciolo resurrected the name of Leonardo Pisano, more than 250 years after the Pisan decree (the last recorded proof that Leonardo was still alive). Pacioli printed a highly regarded, scholarly book titled, Summa de Arithmetica, Geometria, Proportioni et Proportionalita (All That is Known About Arithmetic, Geometry, Proportions, and Proportionality). The Venetian deliberately mentioned Leonardo as his most valuable source, stating, “Since we follow for the most part Leonardo Pisano, I intend to clarify now that any enunciation mentioned without the name of the author is to be attributed to Leonardo” (Devlin, Man 7). Despite this extraordinary endorsement, Leonardo’s contributions to mathematic intelligence lingered in obscurity and “his influence languished for many centuries and indeed Mathematics made no real progress for 300 years” (Horadam).

Fibonacci Statue in Pisa
Fibonacci Statue in Pisa

Then, late in the eighteenth century, another Italian mathematician named Pietro Cossali (1748-1815) came across this single reference to Leonardo in Pacioli’s book. Wondering why Pacioli was famous while the man whose work he “followed” was unknown, Cossali began to look for Pisano’s manuscripts (Devlin, Man 8).

In 1838, French historian Guillaume Libri gave Leonardo the manufactured surname ‘Fibonacci.’ Then, in the 1870s, another Frenchman, the mathematician Edouard Lucas, assigned the name “Fibonacci sequence” to a fascinating number sequence that surfaces when one tries to solve one of the more recreational problems in Liber Abaci (Devlin, Finding 24). Leonardo has been called Fibonacci ever since.

A few memorials commemorate Fibonacci’s contributions to Italy, among them two street names – the quayside Lungarno Fibonacci (Fibonacci Way) in Pisa and the Via Fibonacci in Florence – and a statue of him with a “kind, scholarly expression,” in scholar’s garb, in the Camposanto, a historical cemetery on the Piazza dei Miracoli in Pisa (Devlin, Finding 36, 49).

FIBONACCI’S INTELLECTUAL LEGACY

If what followed Leonardo ‘Fibonacci’ Pisano was an economic revolution, then Liber Abaci was the “gunshot that started the revolution.” There has been discovered in many Italian archives thousands of medieval manuscripts of short, handwritten textbooks in “practical arithmetic” which are so numerous they form their own extensive genre. These manuscripts are called libri d’abbaco (“abbacus books”) or trattati d’abbaco (“abbacus tracts”). “They are written in vernacular Italian, usually in the local dialect of the author. …The earliest of these were handwritten but after the invention of the printing press in the fifteenth century they became recognizable as a genre and some became best sellers.” (Devlin, Finding 25-27) Today there remains more than 400 such texts stretching over 300 years. Part of their significance lies in the quantity; they are proof that their “rapid proliferation” signifies “the importance people attached to learning the new arithmetic.” It is evident that each one was written for a local audience, because the problems they presented were usually expressed in terms of the currency, weights and measures of the local town or region. Some were evidently written by more learned scholars who may well have been teachers who wrote them “to use in classes on practical arithmetic.” Indeed, by the end of the thirteenth century, there were “a number of ‘abbacus schools’ (scuole d’abbaco or botteghe d’abbaco) where ‘abbacus teachers’ (maestri d’abbaco) taught practical arithmetic” (Devlin, Finding 25-27).

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Scholars studying these manuscripts extensively have concluded that it is possible to “construct an ancestral tree of books” leading to the original document, or source, of all the others. Devlin explains, “The entire genre began with a single ‘Abbacus Eve,’ the mother of all abbacus books” and that book, he asserts, is Liber Abaci. He says we know the “Abbacus Eve” was “written by Leonardo himself because no other contemporary mathematician was as accomplished (or he would surely have left his own collection of writings)” (Devlin, Finding 28).

The Hindu-Arabic numerals Fibonacci championed were obviously of inestimable worth to the expanding commercial enterprises of medieval European society. “Of greater importance was the long-range impact on Science and Mathematics of the new system of numeration which he publicized” (Horadam). Nevertheless, few mathematicians over the centuries were aware of his brilliance, most likely because his texts were written in Latin and have remained untranslated into modern languages for so long (eight hundred years!) (Horadam).

Ironically, Fibonacci is known primarily because of the sequence bearing his name “but which he treated only lightly.” Modern mathematicians have named an Association, a Journal, and a Bibliographical and Research Centre after Fibonacci, ensuring that his name (at least one of them) will not be quickly forgotten again (Horadam; Devlin, Finding 37).

 

LEONARDO PISANO: HONORARIUM

To some degree, Leonardo Pisano Bigollo is a forgotten man, for he is primarily obliquely remembered by a name he did not choose. Perhaps he did not expect or desire to be known as a famous mathematician or even a teacher. After all, he deliberately referred to himself as Bigollo in some manuscripts, which could be construed to suggest he was a “man of no importance” (Venetian dialect) or, at the very least, a common traveler (Tuscan dialect) (Livio 93).

It was neither his purpose nor his goal to become famous. Perhaps this humble man methodically and meticulously compiled his mathematics instruction books only to fulfill the terms of a personal purpose which he clearly professes in his autobiographical statement in the Introduction to Liber Abaci (1228):

Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. (Horadam)

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It is surely best to take him at his word when he testified that his intent was to provide for his extended family, his nation, and his people. By working to serve and provide for others, Leonardo’s legacy endures; it is a living history.

Yes, Leonardo Pisano might be remembered primarily as the man with the “Rabbit Problem” or Fibonacci. But at the turn of the thirteenth century in Pisa, a humble mathematician tackled a significant problem stringently and provided the perfect solution: education. Through meticulous writing he equipped Europe for an evolutionary leap of economic consciousness and his instrument (knowledge) would prove to revolutionize the world.

One of the most famous professors in Italian history became an anonymous teacher, a man buried inside the consciousness of countless others, some esteemed, some mere bigollos. Eventually the “forgotten” man became the namesake for a principle in nature, of which we have not yet seen the beginning or end.

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Master Fibonacci: The Man Who Changed Math

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Paperback: 128 pages
Author: Shelley Allen, M.A.Ed.
Publisher: Fibonacci Inc.; 1st edition (2019)
Language: English