The Sorbonne is a world-famous cultural landmark, the heart of French education and a symbol of classical French architecture. You probably don't know everything about the Sorbonne, if...
Technically, it is, but the expression "Sorbonne University", which is often used in Russia and the CIS countries, is not entirely correct. It is correct to say "the University of Paris", and the Sorbonne College was only one of its members back in the eighteenth century.
In the seventies (20th century), the Sorbonne actually "split" into thirteen universities that offer different majors and are located in different quarters of Paris or its suburbs. Only four of the thirteen institutions are still located in the historic buildings of the Sorbonne in the Latin Quarter of Paris. Since then, the universities are called Paris I, Paris II and so on up to Paris XIII.
The number in this case has almost no meaning. The only difference is that the University of Paris I is more like the "very same" Sorbonne, since it specializes in economics, social sciences and law, and Paris XIII teaches exact sciences.