Liberal arts: the trivium and quadrivium
From Severinus Boetius (480-524) derives the term " quadrivium " to indicate the " fourfold road " towards the teaching/learning of the sciences: arithmetic, geometry, music, and astronomy. To the set of non-mathematical disciplines was after given the name " trivium ": grammar, logic, and rhetoric. Starting with Cassiodorus and Isidorus of Sevil, the seven disciplines taken together were defined as " liberal arts ", and for a long while on them relied the attempt to transfer to the new generations the inheritance of the Greek-Roman culture. Still in the 18th century they were at the roots of the Philosophical Faculties, propedeutical courses to the University professional Faculties of Law, Medicine, Theology.
Scientific Revolution: renewal in the trivium and birth of the " Baconian " Sciences
The classical " liberal" education started to clash with some of the results of that complex series of events that goes under the name of " Scientific Revolution ". Not only some of the " classical" sciences of the trivium underwent a basic conceptual modification, but new fields of experimental enquiry emerged: Electricity, Magnetism, Thermology, Chemistry, and some aspects of Optics. These disciplines, defined as " Physica Particularis" in the Aristotelian terminology of the time, Experimental Physics in University courses and " Baconian" sciences by the historian of science Thomas Kuhn, became part of the university programmes in the 18th century. At first they underwent a process of professionalization and quantification and then one of mathematization at the beginning of the 19th century.
Bologna University already in 1737 established chairs of Chemistry and Experimental Physics, but the reforms of Pavia University, a result of the enlightened policies of Marie Therese and Joseph the 2nd of Austria, played a main role in the professionalization of " Baconian Sciences " in the second part of the century. In a few years Pavia University attributed chairs to scientists expert in the new fields and built scientific laboratories and cabinets for them (Volta, Spallanzani, Scopoli, Scarpa and others). The University became one of the best European centres of research.
All over Europe experimentation and quantification grew in the new fields of research, in good tune with the dominant culture of the Enlightenment. New instruments were built and new laws formulated. In the field of electricity famous were the instruments and law of Volta (1782-4) and of Coulomb (1785-7).
Mathematisation of the " Baconian Sciences "
In France, at the military school of Mezieres, after the middle of the century Bossut started to prepare engineers with a deep knowledge of mathematics. Among the students of the time we find Coulomb, Lazare Carnot, Monge. The last two in 1795, during the revolution, were among the founders of the Paris Ecole Polytechnique. The influence of the research and teachings of the School was unmatched: there took place the process of mathematization of the new sciences, mostly through the application of the mathematical theories developed for the classical sciences, namely the potential theory. France rapidly became the leading country for scientific research. A main role was played by the Laplacian research programme, developed in the so-called Societè de lArcueil.
The birth of a Science Faculty at Pavia University
With the French domination (1796-1814) the University of Pavia organisation underwent a major if short lived change. We can see from the general timetable of 1808 (all enclosed in one only page) that the three professional Faculties are now: Sciences, Medicine and Law. The Theological Faculty had been suppressed and the Philosophical (Arts) Faculty in large part shifted to the Licei. The Science Faculty, including the new sciences, acquired an autonomous position (so far Volta had to teach medical students) but was no more part of the cultural propedeutic general background. In a way the liberal arts were split again and the trivium was to mantain a cultural primacy.