With the age of Italian city-states, the society changed profoundly, and with it the request of culture, both in terms of quality and quantity. A sound mathematical competence became mandatory for a growing number of new professions. Accounting skills were requested not only to an accountant but also to handicraftsmen, shopkeepers, architects, as well as the artists of the Humanism and Renaissance. To this latter group belonged Leonardo da Vinci, Raphael, and Michelangelo, just to mention a few.
The reference point of all the abachistic tradition is Leonardo da Pisa, also known as Fibonacci, born in Pisa in 1170. Fibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci (1202) and later named the “Fibonacci numbers” in his honour. The Liber abaci become the “Bible” of the abachists, introducing the written notation for the zero. Luca Pacioli (ca. 1445 – 1517) wrote the «Summa de arithmetica, geometria, proportioni et proportionalita» (Venice, 1494), a textbook for use in the abachist schools in Northern Italy. It was a synthesis of the mathematical knowledge of the time and contained the first printed work on algebra written in vernacular language.