Pacioli did NOT invent the Double-Entry System

One of the great myths, perpetuated by accountants and academics alike, is that modern accounting was a purely European invention by a friend of Leonardo DaVinci's named Luca Pacioli. Ever since I was in school, this myth has been repeated, without primary or secondary sources to lend it any credibility at all. This didn't make sense to me, since accountants had been using double-entry around the world many centuries earlier than the Renaissance. But the accounting profession and academics have steadfastly maintained that modern accounting could only have been a European invention.

I'm here to tell you the real story of the invention of double-entry bookkeeping and modern accounting.

Accounting and auditing are ancient, with many modern practices that are rooted in traditions that date back millennia. This section details the evolution of accounting, with explanations of how historical developments live on in the idiosyncrasies of accounting and auditing today. 

The earliest extant record of humans keeping track of numbers is the Lebombo Bone (several dozen have been found to date) which have been carbon-dated to about 35,000 BC. These are arguably the oldest known accounting computers. They are tally sticks with counting notches carved into a baboon’s fibula, found in the Lebombo mountains located between South Africa and Swaziland.

In the middle of the ninth millennium BCE, communities began coalescing around marketplaces that eventually became the cities of antiquity. Accounting was practiced in the ancient Middle East by means of small counters -- tokens modeled in clay in different shapes, each symbolizing a particular commodity. Their shapes include spheres, flat and lenticular disks, cones, tetrahedrons, and cylinders. These forms seem fully arbitrary and to be dictated only by the concern for making with the least effort. They were easy to identify and duplicate representing daily life commodities.

With stylized signs, all information could be recorded directly on clay tablets, which were cheaper and more portable than tokens. The earliest scribes served as lawyers and accountants in the early cities. They would record trade transactions, debts and advances, in duplicate on clay tablets to be retained by the parties to the transaction. The earliest texts were pictographs on tablets written with a stylus, with accounting-specific writing systems evolving into more expressive systems that described politics, religion, and news. 

Many commodities were exchanged in the early barter communities – silver, grain, and so forth based on standardized weighs, and thus establishing an absolute value for any particular item was complex and inexact. Under King Croesus of Lydia (in modern Turkey) the "touchstone" (mined from local riverbeds) was used to standardize the content of gold alloys, allowing standardized coinage and a single denomination for the price of any item. The earliest coins were blank droplets of metal of standard weight, issued by the treasury; later coins were stamped with punches for easy accounting. It was the custom of unmarried ladies in Lydia to sell their virtue in exchange for coins, in order to accumulate a dowry sufficient for them to marry. In this regard, accounting can credibly lay claim to being "the oldest profession."

The Kingdom of Lydia was short-lived; but their idea of standardized coinage lived on, first in the Athenian silver drachma, and later the Roman Solidus, which provided Mediterranean trade with an unprecedented assurance of quality and value for a numéraire commodity -- one which could be traded with all others. Issuing standardized coinage was a profitable business for the government. Governments essentially take out a non-interest-bearing loans on the money they mint; in turn, this begot profitable industries in money changing, accepting deposits, and lending money at interest. Rome developed sophisticated financial and contracting systems for transport and trade, far-reaching tax collection, and a vast bureaucratic network.  

Parallel developments in Asia saw China evolve from Cowry shells as standard coinage in the fifth century BCE, to copper coins in the Qin Dynasty period (third century BCE). Qin coins were practical -- round with a square hole in the middle (for stringing together) which remained the common design for most Chinese copper coins until the twentieth century. Because of the low value of the coinage, seigniorage and government profit were substantial, as was the tax on transactions. The Qin Dynasty took a no-nonsense attitude towards executing anyone caught making transactions with local coins, or any currency not sanctioned by the government; a policy revived in the Tang Dynasty when they introduced paper (tree bark) currencies.

The Roman Empire sank into medieval chaos after about the third century. Predicting the collapse of civilization, Boethius and Cassiodorus in the 6th century collected existing studies in mathematics (including accounting) into the quadrivium, comprising the four subjects of arithmetic, geometry, music, and astronomy. These were to be taught to Roman patricians in the monastic schools, which before Saint Benedict of Nursia were more or less safe country estates for offspring of the Roman elite. Until the fifteenth century, European accounting was static and unchanged from  Roman practices. Meanwhile in the Middle East, firstly the Umayyad Caliphate, and then the Abbasid Caliphate of Baghdad rapidly gained power over Central Asia by adopting our modern Arabic number system from India. This was a substantial improvement over the cumbersome notation of the Romans. It allowed easier addition and subtractions, as well as allowing accounting to extend itself to multiplication (for prices and cost allocations) and division (for rates). Baghdad became the world’s center of accounting innovations.

In the Islamic world, the word account took on religious significance, relating to one’s obligation to account to God on all matters pertaining to human Endeavour. According to the Qur’an, followers are required to keep records of their indebtedness. Thus Islam provides general approval and guidelines for the recording and reporting of transactions. The Islamic law of inheritance defines exactly how the estate is calculated after death of an individual. The power of testamentary disposition is basically limited to one-third of the net estate (i.e. the assets remaining after the payment of funeral expenses and debts), providing for every member of the family by allotting fixed shares not only to wives and children, but also to fathers and mothers. Clearly this requires ratios, multiplication and division that were well beyond the scope of Roman numerals and abaci.

The complexity of Islamic inheritance law served as an impetus behind the development of algebra by medieval Islamic mathematicians. Al-Khwarizmı’s “The Compendious Book on Calculation by Completion and Balancing” devoted a chapter on the solution to the Islamic law of inheritance using linear equations. In the 12th century, Latin translations of al-Khwarizmı’s “Book of Addition and Subtraction According to the Hindu Calculation” on the use of Indian numerals, introduced the decimal positional number system to the Western world. The development of mathematics and accounting was intertwined during the Renaissance. Mathematics was in the midst of a period of significant development in the late 15th century. Hindu-Arabic numerals and algebra were introduced to Europe from Arab mathematics at the end of the tenth century by Pope Sylvester II and in the twelfth century by Fibonacci.

Al-Khwarizmı (Latinized as "Algorithmi" from which we derived the word "algorithm") introduced algebra (from the Arabic "al-jabr" meaning "restoration”) to accounting, leading to three fundamental accounting-algebreic concepts:

1. Debits = Credits: The 'Bookkeeping equation' for error control, which is the accounting equivalent of algebraic manipulations on the left-hand and right-hand size of an equation.

2. Assets = Liabilities + Owner's Equity: ‘Real’accounts for tracking wealth, and the ‘basic accounting equation’. An elaborate form of this equation is presented in a balance sheet which lists all assets, liabilities, and equity, as well as totals to ensure that it balances.

3. Closing process where ‘Nominal’ accounts for tracking activity are closed to Owner's Equity. Closing out these accounts at year end yields the "net income" (the owner's increment in wealth) -- arguably the most important single statistic produced in the accounting process.

Algebra manipulates formulas around an equal sign, the only constraint being the formula on the right of the equal sign must have the same value as the formula on the left. Double-entry bookkeeping manipulates debit and credit balances around an equal sign, the only constraint being the debits must have the same value as the credits. Accounting is applied algebra. 

Though not specific in this regard, Al-Khwarizmı’s book hinted at what were to become the standards for later accounting: error control (through double-entry) nominal accounts (which appear on the Income Statement), and real accounts (which appear on the Balance Sheet). Nominal accounts are revenue or expense accounts that are closed to a zero balance at the end of each accounting period. They start with a zero balance at the beginning of a new accounting period, accumulate balances during the period, and return to zero at the year-end by means of closing entries. Nominal accounts are income statement accounts and are also called ‘temporary accounts’ in contrast to balance sheet (asset, liability, and owners’ equity) accounts which are called ‘permanent accounts’ or ‘real accounts.’ Real accounts are asset, liability, reserve, and capital accounts that appear on a balance sheet. The balances of real accounts are not canceled out at the end of an accounting period but are carried over to the next period.

Al-Khwarizmı’s method was an immediate hit and was widely disseminated throughout the educated world. In 756, The Abbasid Caliph Al-Mansur sent 4,000 Arab mercenaries to assist the Chinese Tang dynasty in the An Shi Rebellion. After the war, they remained in China and established an alliance with the Tang court where they were known as the Black-robed Arabs. The Tang Dynasty brought in Arab scholars and adopted Abbasid innovations in money and accounting. Trade flourished: the Tangs reopened the Silk Road and hugely expanded their maritime presence into the Persian Gulf and the Red Sea, into Persia’ Mesopotamia’ (sailing up the Euphrates River in modern-day Iraq),into Arabia, Egypt, Ethiopia, and Somalia in the Horn of Africa. They established the most extensive taxation system to date. Each citizen was taxed on iron and salt usage and owed the Dynasty corvee labor of 20 days a year. The state practiced the “equal-field system” in which most land was state-owned and granted to individual farmers to prevent the formation of large estates. This allowed greater government control over the individual farmers but required a huge professional bureaucracy, including accountants selected by Imperial examination. The banknote was first developed in China in the Tang Dynasty during the 7th century, with local issues of paper currency. Its roots were in merchant receipts of deposit as merchants and wholesalers desired to avoid the heavy bulk of copper coinage in large commercial transactions. The Tang dynasty paid local merchants with money certificates called “flying cash”, because of its tendency to blow away. These certificates bearing different amounts of money could be converted into hard cash on-demand at the capital. Since they were transferable, they were exchanged among merchants almost like currency. The threat of penalties and possibly execution also encouraged merchants to use “flying cash.”

The Tang dynasty innovations remained influential long after the dynasty's demise. The Goryeo unification ("Korea" is derived from Goryeo) began in 918 AD. Korea borrowed heavily from the Tang, including the innovation of double-entry accounting which was useful in managing the new national Korean bureaucracy. This knowledge was widely disseminated in Asian after Korea began publishing printed books using sand-casted bronze type around 1200 AD. Japan similarly adopted the Tang's double-entry and other innovations in dress and custom. Al-Khwarizmı’s method was taught throughout the Abbasid empire, in particular in southern Spain. An explosion in the translation and copying of ancient manuscripts from 1200 AD on in Europe included a proliferation of copies of Al-Khwarizmı’s book. It is estimated that around 212,000 manuscripts were copied in 11th century Europe; 768,000 in the 12th; and 1.7 million in the 13th, largely due to the rise of 'universities' (from 'union' and mimicking the structure of the guild unions) and the need for textbooks.  Tang innovations in accounting would have been much less influential were it not for the rise of the Mongol conqueror Genghis Khan and later his grandson Kublai Khan who was deeply influenced by the bureaucracy of the Tang Dynasty. Genghis and his progeny nearly conquered the known world in the thirteenth century. Germany lost nearly a million soldiers (most of its adult males) defending Europe against their invasion. Genghis Khan gave his accountants an unprecedented position of power in the Mongol Empire. When a city was sacked by Mongols, the accountants were the first to enter, tallying up the total asset value of the city (before soldiers could loot or pillage) from which the Mongols took 10%, to be allocated between the troops on well-defined principles. Conquered cities were subjugated, then encouraged to remain going-concerns, so that they could be reliably tithed – in this the accountants also played a pivotal role.

The Caliphate of Baghdad had provided fertile ground for the advancement of mathematics at a time that Europe was stuck in the quadrivium. Many of the ancient libraries of Rome and Greece had been transferred to Baghdad, where scholars integrated the Hindu numerical notation into geometry and the algebra of linear and quadratic equations. These works were disseminated throughout the Abbasid Caliphate, including into Moorish Spain, making this body of knowledge accessible to Europeans in the colleges at Granada, Cordova, and Seville around the beginning of the twelfth century. The Italian mathematician Fibonacci became exposed to this knowledge traveling extensively throughout Egypt, Syria, Greece, and Sicily. He eventually returned to Italy to publish his "Liber Abbaci" (book of calculation) which promoted the use of Arabic numerals for calculations. The book was written in Latin during the year 1202 and was influential and widely read.

The introduction of double-entry bookkeeping into Europe is an interesting one in itself. Arabic numerals were known in Europe, but it was considered sinful to use them. For example, the statutes of the "Arte del Cambio" of 1299 prohibited the bankers of Florence from using Arabic numerals (even though they had been slipping them into documents since the tenth century just to ease calculations). Pope Sylvester II who reigned for three years at the turn of the millennium, endorsed and promoted the study of Arabic arithmetic, mathematics, and astronomy, reintroducing the abacus to Europe. After his death, he was widely denounced as a sorcerer in league with the devil for exactly this reason.

It was into this politically and religiously charged atmosphere that the innovations in Fibbonaci’s "Liber Abbaci" started merchants and bankers synthesizing alternatives to the abacus and daybooks of unwieldy Roman numerals. Fibbonaci himself was a merchant as well as a mathematician. He traveled extensively throughout the Mediterranean as a merchant prior to 1200. Not only did he encourage the adoption of the Hindu-Arabic numerals for commercial accounting, but he actually set out an account contrasting completely the Roman figures versus the Arabic numerals.

Importantly, the Hindu-Arabic system mathematics also covered systems of equations, and these were in addition introduced into Spain by the Moors. From an accounting perspective, the conceptualization of debits and credits provided a generalization at the accounting systems (financial statement) level in addition to details at the transaction (journal entry) level. Equations -- by definition -- require equality of two sides of the equation -- on one side dependent variables, on the other independent. In an exchange transaction, there is a natural dichotomization into independent variables (assets) and dependent variables (claims). These are reflected in the Latin words debere (to owe) and credere (to entrust), which are the basis for our modern words, debit and credit.

The Hindu-Arabic system systems of equations were focused on equilibrium - in the balance sheet at any date, an equilibrium of exchange transactions is preserved. The use of an equilibrium device may at first have been "pro forma". But it is easy to see how that the change from ad hoc single-entry to equilibrium bookkeeping could lead to a complete double-entry system (particularly given European bankers’ early penchant for slipping Arabic numerals into their financial records, despite the fact that they might be accused of colluding with the devil). Once figures began to be disposed in a single column, instead of being scattered all over the page and reduced to order only outside the account-book on the abacus or in the mind, then the advantages of having two clearly separated columns, simply to facilitate computation, would quickly become apparent.

For two centuries, during the rise of the great Italian banking centers of Genoa, Florence and Venice, Italian banking recorded transactions, made loans, issued script, and numerous other activities that we would recognize today. Initially, they used single-entry recording (date, and account affected) but this proved error-prone as transaction volume increased. Fibbonaci’s Liber Abbaci was widely read, and influential. Giovanni di Bicci de’ Medici introduced double-entry bookkeeping for the Medici bank in the 14th century. By the end of the 15th century, merchant ventures in Venice used this system widely.

The 15th century also saw the invention of the printing press in Germany, and affordable, widely available reading glasses from Venetian glassmakers. Leo X’s Vatican was an enthusiastic customer, where printing presses were used to churn out indulgences, and subsequently, Italy became a center of printing, book publishing and literature. One of the first great texts on mathematics was published by a close friend of Leonardo da Vinci, Venetian Luca Pacioli, in 1494. "Summa de Arithmetica, Geometria, Proportioni et Proportionalita" (Everything About Arithmetic, Geometry and Proportion) formally described the widely used but still controversial system of double-entry for a much wider audience. Pacioli’s Summa included one chapter titled Details of Accounting and Recording that popularized the Method of Venice for accounting (an evolution of Al-Khwarizmi’s method). Pacioli’s Summa described the components of bookkeeping as: a memorandum book, journal, and ledger, with the journal and ledger similar to modern equivalents. A trial balance was used when the books were closed. The profit or loss was entered into the capital account to balance the balance sheet. Thanks to Gutenberg’s printing press, Summa was published throughout Europe.

Pacioli’s Summa was translated into the most commonly read vernaculars in Europe, and was influential not only in investment and merchant ventures but in accounting in the great estates of Europe. Over the next four hundred years, it became the standard, in only slightly modified form, for accounting in all realms of business in Europe. Before the Industrial Revolution, China and India were the wealthiest economies in the World. Mughal India’s annual revenues were twenty times that of France. In China, Qianlong demanded that Britain’s ambassador Lord McCartney kowtow, and informed him that China was in need of nothing from the West. Europe was only a minor economic player in the World at the start of the Industrial Revolution in the late eighteenth century.