Though generations of schoolchildren have cursed arithmetic, the world was a much more inconvenient place without it. Before the advent of modern arithmetic in the 13th century, basic calculations required a physical abacus.
But then came a young Italian mathematician named Leonardo da Pisa — no relation to da Vinci — who, in 1202, published a book titled Liber Abaci. That's Latin for "Book of Calculation."
And though it doesn't necessarily sound like an overnight best-seller, it was a smash hit. Liber Abaci introduced practical uses for the Arabic numerals 0 through 9 to Western Europe. The book revolutionized commerce, banking, science and technology and established the basis of modern arithmetic, algebra and other disciplines.
Weekend Edition "Math Guy" Keith Devlin tells the story of this arithmetic revolution in his new book, The Man of Numbers. Numerals 0 to 9 had been around in Hindu and Arabic cultures for centuries, but the problem was, Europeans didn't really do business with the numbers.
"They recorded everything in good old Roman numerals and if they wanted calculations, they went down the street to someone who was adept at using a physical abacus," Devlin tells NPR's Scott Simon. "It was actually a board with lines on it on which you moved pebbles around; it was a crude and inefficient way of doing business."
The first edition of Liber Abaci was a dense, detailed book that was hard for the average person to grasp. So da Pisa released a simplified version to reach the traders and commercial people of Pisa — and the result spread around the world.
"Within a few decades of Liber Abaci appearing you've got what may have been 1,000 or more different people writing practical arithmetic textbooks," says Devlin. "Ordinary people who wanted to set up a business — and didn't have a lot of money to pay people to do the accounting for them — could do it for themselves."
The basics of accounting, banking, insurance and double entry bookkeeping all came out of 13th century Pisa, Devlin says. And that was thanks to the new ability to do arithmetic efficiently.
Sure, basic arithmetic may seem a simple thing today, but Devlin says its introduction to the world was comparable to the invention of the computer. Tedious and complicated tasks that required a specialist were suddenly faster and easier — and something you could do for yourself. "[Da Pisa] is Steve Jobs, Bill Gates. It's the computer revolution that we lived through in the 1980s, and the parallels are actually uncanny," says Devlin.
Despite his lasting impact on the modern world, da Pisa is not exactly a household name. But you might recognize him by his nickname: Fibonacci. In addition to writing Liber Abaci, da Pisa also introduced the famous Fibonacci sequence to Western Europe. (Remember that one from high school math? It starts with 0 and then 1, and then every subsequent number is the sum of the two numbers that precede it.) The name was given to him by a historian in the 19th century who read the phrase filius Bonacci — "son of Bonacci" — at the beginning of Liber Abaci and gave da Pisa his moniker.
Although Fibonacci can take credit for practical arithmetic in the Western world, Devlin says that even without him, it's unlikely that people would have had to rely on the abacus forever.
"One of the things about almost all of mathematics is that it will eventually surface and get used," Devlin says. "It's a matter of who does it and when."
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