The historical significance of Double-Entry bookkeeping can not be understated. Prior to Leonardo "Fibonacci" Bonacci bringing it to Pisa from the Arabs in Algiers, North Africa, there was no concept of "budget" for most merchants, each transaction was a separate affair, and consequently, finance could not scale. There were several attempts at international lending, and it bankrupted the Bardi and Paruzzi companies who lent lots of money to King Edward III, who ended up defaulting on it. The Medici family succeeded where others failed, providing a level of service in banking previously unparalleled, thanks to being able to manage complex cash flows through Double-Entry bookkeeping. (Fibonacci also introduced the Hindu-Arabic numeral system at a time where most of Europe was using Roman Numerals for arithmetic). It made the Republican city states of northern Italy on par with the political power of noble families, and as other countries caught up with Florence, one could, for the first time, seek an education outside of the Church and in their own country.

Every programmer should be familiar with one descendant of double-entry bookkeeping: the integer. Though its binary representation may be more familiar, the formal mathematical construction of the integers consists of an equivalence class of pairs of natural numbers. In the Chinese "Nine Chapters on the Mathematical Art" they describe red and black counting rods denoting gains and losses, and the equivalence class being that taking away a red and black rod at the same time leaves the "total" or normalized form unchanged. Integers took a lot of time to be accepted in mathematical practice, but they were in use for far longer.