How the world’s first business bestseller transformed the world

Learn from the world’s biggest business thinkers.

In 1202, having spent years learning the secrets of Saracen magic from the traders of Bejaia and witnessing algebra in commercial action on the docks of Messina, Leonardo of Pisa — the man who we know as Fibonacci — published the book that would transform commerce in Europe. It was called Liber Abaci, The Book of Calculations, and in it Fibonacci set out algebraic principles that, essentially, enabled merchants to make money. He had the journalistic gift of making the strange seem commonplace and the tangential seem relevant. By posing real-life examples of conundrums faced by traders, Fibonacci brought maths to life. Had he written in the language of the academy, the book would have had limited relevance. But because he wrote it for the merchants, Fibonacci revealed the true genius of the great teacher: an ability to escape from the tyranny of his peer group. If he had tried to convince the scholarly monks, his work would have been picked apart by vindictive ‘experts’ and its credibility undermined. Taking the route of all great communicators, Fibonacci sidestepped the gatekeepers and went straight to those who would get the most value from this new technology: the merchants.

Liber Abaci became the go-to book for traders and an essential tool of international commerce. It could be regarded as the first bestselling business book. Revelatory as well as revolutionary, it explained how to calculate interest rates, how to circumvent the Church’s usury laws, apportion profits, and assess revenues and costs. It gave merchants a roadmap to express their produce in terms of someone else’s products, in fractions and in a common currency. The fact that the book devoted many pages to puzzles regarding interest rates, banks and usury made it quite provocative: the Church looked unfavorably on it as a challenge to its monopoly on the money-lending business. Condemning moneylenders to hell is a pretty good way of protecting your turf: damnation has the added upside of never being challenged in court. Of all those most threatened by the financialization of European small business, the biggest, most successful and longest-surviving multinational the world had ever seen, the Church, with its corporate headquarters in Rome, had a lot to be worried about.

One of Fibonacci’s most consequential insights concerned the relationship between money and time. He teased out what economists call the time value of money, which is better understood as the financial equivalent of ‘it’s better to have an egg today than a chicken tomorrow’. This idea that money today is better than a promise of money tomorrow is what underpins all borrowing and lending. It’s what we call the opportunity cost. If I lend to you, it means that you have the money and I can’t use it, so there is a cost to me. The money I earn back from you after you pay me back must be adjusted for the opportunity that I have forgone. The way to calculate this is to divide all the money I get back from you by the prevailing interest rate. Why the interest rate? Because the interest rate is what I would have got by simply keeping my money on deposit. We all intuitively understand that now, but back then, giving money a value over time was revolutionary. It also allowed merchants and bankers to discriminate between various projects that they were being asked to finance. The Sumerians had introduced interest rates thousands of years previously, but Fibonacci made the time value of money more accessible by setting this theory out in algebraic terms that were easy to calculate. Fibonacci’s clarity brought these ideas to both the merchant class and the banking class. And it led, inexorably, to their combination: the merchant banker.

Back then, giving money a value over time was revolutionary.

The Pucci Palace in Florence, dating back to the fourteenth century, has extraordinary rooftop views of Brunelleschi’s cathedral dome. Whatever you say about the Florentine merchant princes, they were good at holding onto their brass. The palazzo’s library contains vast archives with ledgers, documents and correspondence to and from merchants, agents and buyers across the world. The Florentine merchant was a committed letter writer and underpinning most of these letters was the ledger, containing the balance sheets of a whole host of businesses. The balance sheet was the main weapon of the new class of merchants, and it would never have come about were it not for Fibonacci’s numerical evangelism.

Writing about 200 years after Fibonacci, the monk Luca Pacioli (who taught mathematics to both Leonardo da Vinci and Albrecht Dürer) described the ‘Italian’ approach to bookkeeping. This double-entry bookkeeping revolved around having a set of accounts, drawn up by merchant bankers and their clerks, for households, companies and wealthy individuals, set out in debits and credits. Each debit had to have a corresponding credit on the balance sheet and at the end of whatever period they were measuring, these accounts had to balance. Once the accounts were settled and everyone was paid, the process could start again. Obviously, fastidious double-entry bookkeeping reduces the margin for error, even in complicated accounts, but more than that, once accounts become commonplace, ordinary people begin to think of the world in terms of accounts. Today, it is not unusual to hear national news broadcasts refer to the ‘current account’ of the country — never mind a company, a football club or a household. This way of looking at the world, which is unlike anything that went before, began with Fibonacci’s introduction of ‘Saracen magic’ to Europe.

Possibly Liber Abaci’s most profound ramification was as intellectual as it was practical: it nudged more and more people towards reasoned, quantitative enquiry. At the core of quantifiable mathematics is the notion of precision. The ledger is the foundation of reasoned conclusion. As they say: the numbers don’t lie. The old world was one of conjecture, miracles and guesswork. Fibonacci’s new world rested on objective, quantifiable value and empiricism — a novel and fundamental concept. The human mind’s capacity to reason with precision is one of the great breakthroughs in our comprehension of the world around us. Mathematics is the technology that allows us to move from the vague to the meticulous, from nebulous guesswork to exact fact. Fibonacci changed how we learned, taught and calculated. The feudal economy was giving way to another age: the Age of Money.

At the core of quantifiable mathematics is the notion of precision. The ledger is the foundation of reasoned conclusion. As they say: the numbers don’t lie.

God-fearing Florentines initially banned Arabic numerals, but suppression rarely works, particularly if a new technology is capturing people’s imaginations. It is impossible to stop a powerful technology. Even more critically, it is impossible to stop a powerful technology that enables people to make money. By the end of the thirteenth century the Florentines realized their folly and, as commercial players, introduced zero to their world through special business schools. By 1350, Hindu- Arabic mathematics was so popular that over a thousand pupils within the walls of Florence were attending special ‘reckoning schools’. These reckoning schools, the Harvard MBAs of the fourteenth century, were based on the transformative mathematics of Fibonacci. Just as MBAs worldwide have spawned a managerial caste — the foot soldiers of the corporate world — the reckoning schools produced their own commercial caste. Notable pupils of these Florentine schools were Niccolò Machiavelli and Leonardo da Vinci. Even Dante Alighieri, great critic of the bankers’ excess in Florence, sent his son to such a school to learn the dark arts of commerce.

Having numbers, balance sheets and mathematics was one thing, but to get the best use of these innovations, the Florentines developed a stable currency they could believe in, one that would give merchants confidence and security. A new sort of money was entering the world via Florence. And Dante, Florence’s most famous son, saved a special place in his Inferno for those who abused it.

Learn from the world’s biggest business thinkers.

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