![]() But there is a reason why people hardly ever give any thought to just how revolutionary, in their time, were numbers (and the associated innovation of money), arithmetic, the Hindu-Arabic representation, the classical arithmetic algorithms, and algebra. Given my experience with al-Khwārizmī and Leonardo, I should have known better. It’s just keeping records, right? What’s the big deal? Double-entry book-keeping, on the other hand, the one topic Pacioli covered that those previous authors had not, simply never caught my attention. Fibonacci) while I was researching my three books on Leonardo and his hugely influential mathematics text Liber abbaci (the project began with a single book in mind), I had long ago come to appreciate the magnitude of the mathematical developments those two authors had catalogued-and thereby contributed to-in terms both of human intellectual progress and the impact of those methods on the way people around the world go about their daily lives. Having spent time studying both al-Khwārizmī and Leonardo of Pisa (a.k.a. Excel is a digital implementation of ninth century commercial arithmetic and algebra, as laid out by al-Khwārizmī in his two famous books on the subjects QuickBooks an implementation of the book-keeping methods described by Pacioli in Chapter 9 of Summa. As a result, I long ago started keeping meticulous records, using Excel spreadsheets to keep track of individual activities and QuickBooks to bring it all together. I have several sources of income from around the world-from my university position and my ed tech startup company BrainQuake fees from writing, speaking, and consulting royalties from books and more recently income from a number of pensions and annuities. Though by no stretch of the imagination am I in the big-income category, my tax-filing situation is not simple. Indeed, I spent several days in March going through my QuickBook records as I prepared my annual tax filing. ![]() ![]() Sure, I knew what double-entry book-keeping was. (I also gave a talk at a public showing Christie’s organized in San Francisco on April 24, which gave me an opportunity to examine the book myself.) Neither did I-until I was asked to write a brief article about the fifteenth century Italian mathematician Luca Pacioli, to go into the sale catalog for the upcoming (June) Christie’s auction of an original first edition of his famous book Summa de arithmetica, geometria, proportioni et proportionalita (“Summary of arithmetic, geometry, proportions and proportionality”), published in 1494, which I referred to in last month’s column. What’s your reaction when you see the term “double-entry book-keeping”? Do you associate it with cool, societal-changing innovations like the Internet, Google, social media, laptops, and smartphones? Probably not.
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