Fibonacci is credited with the introduction of Arabic arithmetic to Europe. Did he tried hard to share this knowledge with other mathematicians? With whom? How did they react?

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    $\begingroup$ MIght be better worded as "What actions and communications did Fibonacci undergo ..." . BTW, it's always to provide a citation of a claim. That at least gives interested readers a starting point. $\endgroup$ Commented Apr 13, 2020 at 13:30
  • $\begingroup$ @CarlWitthoft Thanks for your guidance. $\endgroup$ Commented Apr 13, 2020 at 14:02
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    $\begingroup$ Fibonacci wrote a book on the subject. It is called Liber abaci (book of abacus). $\endgroup$ Commented Apr 13, 2020 at 15:08

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Sharing with other mathematicians is not how things were done in the 13th century Europe. The only other mathematician of note in Europe whose years of life overlap with Fibonacci's was Nemorarius (1225-1260), and he was not even born when Liber Abaci came out (1202). Nonetheless, Fibonacci was quite active in promoting mathematics both to the folk and to the learned, those who were around, and he had a knack for popularization of mathematics in applications.

MacTutor's biography is quite informative in this regard. For example, he corresponded with Michael Scotus, the astrologer, Theodorus Physicus, the philosopher, and Dominicus Hispanus since his return to Pisa c. 1200. This got him a favorable reception at the court of Frederick II, who became the Holy Roman emperor in 1220, and spent most of 1220s in Italy solidifying his control there. Frederick was a benefactor of scholars and founded the University of Naples in 1224. Johannes of Palermo, a Frederick's courtier, presented a number of problems to Fibonacci, which he solved and published in Flos (1225), adding to his fame. Liber Abaci itself was presciently dedicated to Scotus, who became the court astrologer. Its second section contained problems concerning the price of goods, calculating profits on transactions, and converting between currencies, clearly designed to make the decimal system attractive to merchants.

Fibonacci also wrote a separate book on commercial arithmetic Di Minor Guisa, which is not extant. His Practica geometriae (1220) had a similarly practical bent. Liber Abaci became quite popular with the folk as well as the court, and so did Fibonacci. In 1240 his home city of Pisa awarded a salary to "the serious and learned Master Leonardo Bigollo" ("Fibonacci" is a nickname invented by a historian Libri in 1838) for his troubles with advising and teaching the citizens new ways of accounting and land surveying. Vogel in the Dictionary of Scientific Biography writes the following on his influence:

"Direct influence was exerted only by those portions of the "Liber abaci" and of the "Practica" that served to introduce Indian-Arabic numerals and methods and contributed to the mastering of the problems of daily life. Here Fibonacci became the teacher of the masters of computation and of the surveyors, as one learns from the "Summa" of Luca Pacioli..."

However, as Schaller points out in Fibonacci, Pacioli, and the Slow Diffusion of Knowledge, comparison to Pacioli also shows limitations of Fibonacci's efforts, which explain why decimal calculations did not spread widely until 16th century:

"In the 1460s, while Luca Pacioli, a Franciscan monk, was working in Venice, he discovered a copy of Fibonacci's Liber Abaci. Because he had worked six years as a merchant's assistant, Pacioli was able to recognize the importance of the book for the practical world of business... Pacioli's summary of contemporary mathematical knowledge appeared in 1494 under the title Summa de arithmetica, geometria, proportioni, et proportionalita...

There are two key differences between Fibonacci's Liber Abaci and Pacioli's Summa, despite the fact that the intellectual content of Pacioli's chapters on Arabic numerals and the basic principles of arithmetic follow Fibonacci's book very closely. First, the Summa was printed, rather than handwritten. The dramatic decrease in cost made it possible for merchants to buy the book. Second, Pacioli wrote almost all of his book in the vernacular, making it accessible to business people."

  • $\begingroup$ Why "Fibonacci is a nickname invented by a historian Libri in 1838"? Actually Libri was a very sensible historian, more than Montucla, for sure. Bonacci/Fibonacci was already used by e.g., Cossali (1797): he call him Leonardo Bonacci, and also Leonardo di Bonacci (which means "Leonardo of the Bonacci family", and so fi(lius)Bonacci), and somewhere Leonardo di Pisa or simply Leonardo. "Bigollo" is not a surname/family name, but a nickname: bigollo/picollo means "spinning-top" (see Cecco), and the sense is that he was a traveller. $\endgroup$
    – user6530
    Commented Apr 17, 2020 at 15:21
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    $\begingroup$ The oldest explicit reference to "Fibonacci" I can find is in Flaminio del Borgo, Dissertazione epistolare... (1765). Also before Libri: Grimaldi, Memorie istoriche di più uomini illustri pisani (1792); Michaud, Biographie universelle (1811-18); Ersch&Gruber, Allgemeine Encyclopädie der Wissenschaften und Künste (1818); Leslie, The philosophy of Arithmetic; Chasles, Aperçu historique sur l'origine...(1837), and many others. After Libri: de Morgan, Arithmetical books... (1847). $\endgroup$
    – user6530
    Commented Apr 17, 2020 at 15:52

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