What Leonardo did was every bit as revolutionary as the personal computer pioneers who in the 1980s took computing from a small group of “computer types” and made computers available to, and usable by, anyone. Like them, most of the credit for inventing and developing the methods Leonardo described in Liber abbaci goes to others, in particular Indian and Arabic scholars over many centuries. Leonardo’s role was to “package” and “sell” the new methods to the world.
The appearance of Leonardo’s book not only prepared the stage for the development of modern (symbolic) algebra, and hence modern mathematics, it also marked the beginning of the modern financial system and the way of doing business that depends on sophisticated banking methods. For instance, Professor William N. Goetzmann of the Yale School of Management, an expert on economics and finance, credits Leonardo as the first to develop an early form of present-value analysis, a method for comparing the relative economic value of differing payment streams, taking into account the time-value of money. Mathematically reducing all cash flow streams to a single point in time allows the investor to decide which is the best, and the modern version of the present-value criterion, developed by the economist Irving Fisher in 1930, is now used by virtually all large companies in the capital budgeting process.
What Leonardo brought to the mathematics he learned in Bugia and elsewhere in his subsequent travels around North Africa were systematic organization of the material, comprehensive coverage of all the know methods, and great expository skill in presenting the material in a fashion that made it accessible (and attractive) to the commercial people for whom he clearly wrote Liber abbaci. He was, of course, a highly competent mathematician — in fact, one of the most distinguished mathematicians of medieval antiquity — but only in his writings subsequent to the first edition of Liber abbaci in 1202 did he clearly demonstrate his own mathematical capacity.
Following the appearance of Liber abbaci, the teaching of arithmetic became hugely popular throughout Italy, with perhaps a thousand or more hand-written arithmetic texts being produced over the following three centuries. Moreover, the book’s publication, and that of a number of his other works, brought Leonardo fame throughout Italy as well as an audience with the Holy Roman Emperor, Frederick II. Since the Pisan’s writings were still circulating in Florence throughout the fourteenth century, as were commentaries on his works, we know that his legacy lived on long after his death. But then Leonardo’s name seemed to be suddenly forgotten. The reason was the invention of movable-type printing in the fifteenth century.
Given the Italian business world’s quick adoption of the new arithmetic, not surpisingly the first mathematics text printed in Italy was a 52-page textbook on commercial arithmetic: an untitled, anonymous work known today as the Aritmetica di Treviso (“Treviso Arithmetic”), after the small town near Venice where it was published on December 10, 1478. Soon afterwards, Piero Borghi brought out a longer and more complete edition, printed in Venice in 1484, that became a true bestseller, with fifteen reprints, two in the 1400s and the last one in 1564. Filippo Calandri wrote a third textbook, Pitagora aritmetice introductor, printed in Florence in 1491, and a manuscript written by Leonardo Da Vinci’s teacher Benedetto da Firenze in 1463, Trattato d’abacho, was printed soon afterwards. These early printed arithmetic texts were soon followed by many others.
Though Liber abbaci was generally assumed to be the initial source for many, if not all, the printed arithmetic texts that were published, only one of them included any reference to Leonardo. Luca Pacioli, whose highly regarded, scholarly abbacus book Summa de arithmetica geometria proportioni et proportionalità (“All That Is Known About Arithmetic, Geometry, Proportions, and Proportionality”) was printed in Venice in 1494, listed Leonardo among his sources, and stated: