A youth who had begun to read geometry with Euclid of Alexandria, mathematician, teacher at the Alexandrian Library under the reign of Ptolemy I, when he had learnt the first proposition, inquired, "What do I get by learning these things?" So Euclid called a slave and said "Give him three-pence, since he must make a gain out of what he learns. There is no other Royal path which leads to geometry". (Stobaeus, Extracts). It is not known if the anecdote is true but it is significant of the fact that mathematics in old Greece was conceived as totally far from any practical application.

		It is common knowledge that geometry was born in Egypt for the fields measurement. Among the Greeks made the qualitative leap becoming pure science through the idealization of the geometric entities. It is true that thanks to Archimedes even the Greek mathematics was applied to physics and engineering, nevertheless if we refer to the use of the mathematics to the economics, commercial, professional activities, to architecture, to the military field, to the measurement equipments, i.e. to large scale application, we have to wait until the XIII century in Italy to see its origins and diffusion.
With the age of Italian city-states, the society changed profoundly and with the society changed the request of culture both in quality and quantity. A mathematical base became the needed backing to the growing number of professions that were beginning to take shape. Accounting skills were requested not only to the accountant but also to the handicraftsmen, the shopkeepers, the architects, the artists of the Humanism and Renaissance. To this cultural stratum belong Leonardo da Vinci, Raphael, Michelangelo, just to mention a few. The reference point of all the abachistic tradition is Leonardo da Pisa known also 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 honor. The Liber abaci become the "Bible" of the abachists. This book is also celebrated because it introduces 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 abbaco schools of Northern Italy. It was a synthesis of the mathematical knowledge of his time and contained the first printed work on algebra written in the vernacular.
Gerolamo Cardano (1501-1576), professor at the Universities of Bologna, Pavia and Milano, wrote in latin in the 1539 the Practica arithmetice et mensurandi singularis. Also Christoph Kalu (Cristoforo Clavio) (1537-1612) was a distinguished mathematician of the Compagnia di Gesù (Society of Jesus). He was scientific advisor of the pope Gregory XIII for the calendar reform, maintaining relationship with the most important scientists of his time, such as Galileo Galilei, Tycho Brahe, Johannes Kepler, Francesco Maurolico, Frederico Commandino.
		He wrote the Aritmetica pratica, in latin in 1583 and in vernacular in 1586. The abbaco schools represent a cultural change of the mathematical fruition. What does this cultural change consist of? For the first time the mathematics enter extensively in the professional activity. How much of mathematics is needed by an artilleryman? A captain? An agronomist, an architect, a painter? And, we may say today, how many tools that may help to understand and use the technology are needed in the world?