The so-called Renaissance was an epoch in the European history from the 14th to the 17th century, connecting the Middle Ages and modern history. The name "renaissance'' reflects the "rebirth'' of culture (and later science), starting in Italy and later in other parts of Europe. The first European universities were founded (in Bologna already in the 11th century, followed by Paris and Oxford in the beginning of the 13th century. In the next decades several further universities in Italy, France, Spain, and Germany started their business; Würzburg University was first opened in 1402, however, it was closed only about a decade later in 1413 due to financial problems and murder of the chancellor; in 1582 the institution was re-opened). At that time, quite a few researchers were working as clerics, e.g., Nicolaus Copernicus was a canon (priest) at Frombork (Poland), where he established his idea of the heliocentric model of our solar system just before his death in 1543, and Pierre de Fermat earned a living as a lawyer in Toulouse, in 1652 being promoted to the highest level at the criminal court. Moreover, there was no clear distinction between different subjects, Galileo Galilei, famous for his work in astronomy, was appointed the chair of mathematics at Pisa in 1589, and Isaac Newton got the Lucasian Chair of Mathematics in Cambridge in 1663; both are nowadays famous with respect to their works in physics.

Here we shall focus on the mathematicians Rene Descartes, Blaise Pascal, and Pierre de Fermat; the three of them were playing a central role in the development of analytic geometry.