A mathematician from Pisa
Leonardo of Pisa, known today as Fibonacci, was born around 1170. His father worked for Pisan merchants at a trading post in Bugia, a port in North Africa now called Bejaia in Algeria. There the boy learned the methods of calculation used by local merchants, which relied on nine Indian digits and a sign for zero. Later he travelled around the Mediterranean, and, by his own account, saw different calculation methods in places such as Egypt, Syria, Greece and Sicily and judged the Indian method the best.
The name “Fibonacci” is a later nickname, and it seems to have become common only centuries after his death. During his lifetime he was known as Leonardo, with various family labels attached.
What Liber Abaci was
In 1202 Leonardo completed a Latin book called Liber Abaci. The title is often translated “Book of Calculation”, and it should not be confused with a manual about the abacus. In medieval Italy the word “abacus” had come to mean calculation in general, and the book actually teaches calculation with pen and paper using the Hindu-Arabic digits.
The book begins with the digits themselves. Leonardo introduces the nine figures and the sign for zero, explains how place value works, and then shows how to add, subtract, multiply and divide with them. It goes on to fractions and, at great length, to practical problems of the kind merchants faced: converting between currencies and weights, working out prices and profits, dividing shares in a partnership, and calculating the value of alloyed metals. Later chapters turn to more theoretical puzzles and some algebra. A revised version appeared around 1228.
One puzzle in the book, about the breeding of rabbits, gives a sequence of numbers in which each is the sum of the previous two. Those numbers now bear his name, but the Fibonacci sequence was known in Indian mathematics earlier, and the rabbit problem was an exercise, not a claim about biology.
Not the first, but the most influential
It is sometimes said that Fibonacci introduced Arabic numerals to Europe. That is too simple. Knowledge of the digits had reached parts of Europe earlier. A tenth-century manuscript from Spain, the Codex Vigilanus, shows the nine Indian figures without a zero, and later writers connected scholars such as Gerbert of Aurillac with the early teaching of the digits, though details of his role are discussed. Translations of Arabic mathematical works, including a Latin text based on the work of al-Khwarizmi, spread the methods in learned circles during the twelfth century.
What Liber Abaci added was breadth and a practical audience. It was long, it was thorough, and it was aimed at people who handled money and goods. Its worked examples showed that the new methods saved effort and allowed a written check of results. Copies circulated in Italy, and later authors of commercial arithmetic books borrowed from it or built on its approach.
Why adoption was slow
The new digits did not win at once. There were several reasons.
- Familiarity. Roman numerals were deeply established in records, accounts and monuments, and they are still seen on clocks today. Reckoners used counting boards and an abacus to do the arithmetic, then wrote the result in Roman numerals, so the notation did not need to be convenient for calculation.
- Teaching traditions. Two groups were sometimes described as rivals: the abacists, who used the board, and the algorists, who calculated with the new digits. Their competition lasted for generations.
- Suspicion of change. There were worries about forgery and error. The digit 0 could be turned into a 6 or a 9, and a few extra strokes could alter a figure. A rule often cited from Florence in 1299 is said to have restricted the use of the new numerals in certain bankers’ documents, though the surrounding details are debated.
- Handwriting. Digit shapes were not standard. Before printing, copyists drew them in varied ways, and the sign for zero was unfamiliar enough that many people did not understand it well. The history of zero shows how long its full meaning took to settle.
The old finger reckoning of medieval schools, which let monks and clerks represent numbers on their hands, also continued alongside written methods.
Printing and standardisation
The balance changed gradually over the following centuries. Commercial arithmetic books in Italian and other languages taught merchants’ sons the new methods, and from the later fifteenth century, printed arithmetic books helped to fix the shapes of the digits. By the sixteenth and seventeenth centuries, Hindu-Arabic numerals had become the usual choice for calculation in much of Europe, while Roman numerals remained for dates, chapter numbers and ceremonial use.
The lasting picture
The story of the digits in Europe is less a single moment than a long, uneven process involving translators, teachers, merchants and printers. Fibonacci’s book is a convenient landmark because it gave the new method a thorough European exposition. The digits it taught trace back to earlier Indian forms, and the shapes that Europe received came by way of North African Arabic-writing scholars, which is why the shapes used in the West differ somewhat from those in the eastern Arabic script. How those shapes first developed is the subject of the history of Brahmi numerals.