The Man of Numbers Quotes

“When he was about fourteen years of age, Leonardo would have left the fondaco and most likely traveled with an older merchant, a form of apprenticeship system common in those days. Around that time his father summoned him to Bugia. No one knows exactly when he made this voyage. In the introduction to Liber abbaci, he later wrote: “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.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“Underlying all this activity—in the customhouses, on the wharves, in every place of business—were numbers. Merchants measured out their wares and negotiated prices; customs officers calculated taxes to be levied on imports; scribes and stewards prepared ships’ manifests, recording the values in long columns using Roman numerals. They would have put their writing implements to one side and used either their fingers or a physical abacus to perform the additions, then picked up pen and parchment once again to enter the subtotals from each page on a final page at the end. With no record of the computation itself, if anyone questioned the answer, the entire process would have to be repeated.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“A significant difference between Pacioli’s book and Treviso Arithmetic is that Pacioli dealt with negative numbers. The concept of negative numbers was new in Europe, and Pacioli is believed to have provided the first printed explanation.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“In chapter 10, he explained how to use similar methods to manage investments and profits of companies and their members, and showed how to decide who should be paid what.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“Having described the basic methods of Hindu-Arabic arithmetic in the first seven chapters, Leonardo devoted most of the remainder of the book to practical problems. Chapters 8 and 9 provide dozens of worked examples on buying, selling, and pricing merchandise, using what we would today call reasoning by proportions—the math we use to check the best deal in the supermarket.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“European scholars had translated into Latin two important Arabic manuscripts, written by the ninth-century Persian mathematician Abū ‘Abdallāh Muammad ibn Mūsā al-Khwārizmī (ca. 780–ca. 850 CE).”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“The choice of ten basic number symbols—that is, the Hindus’ choice of the base 10 for counting and doing arithmetic—is presumably a direct consequence of using fingers to count. When we reach ten on our fingers we have to find some way of starting again, while retaining the calculation already made. The role played by finger counting in the development of early number systems would explain why we use the word “digit” for the basic numerals, deriving from the Latin word digitus for finger.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“The number system we use today—the Hindu-Arabic system—was developed in India and seems to have been completed by around 700 CE. Indian mathematicians made advances in what would today be described as arithmetic, algebra, and geometry, much of their work being motivated by an interest in astronomy. The system is based on three key ideas: notations for the numerals, place value, and zero.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution

“By the latter part of the first millennium of the Current Era, the system we use today to write numbers and do arithmetic had been worked out—expressing any number using just the ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and adding, subtracting, multiplying, and dividing them by the procedures we are all taught in elementary school. (Units column, tens column, hundreds column, carries, etc.) This familiar way to write numbers and do arithmetic is known today as the Hindu-Arabic system, a name that reflects its history.”
― Keith J. Devlin, The Man of Numbers: Fibonacci's Arithmetic Revolution