A sketchy story of mathematics at Charles-Ferdinand University
The University of Prague was created in 1348 after an imperial decree of Charles IV. It included four nationes: the Bavarians, the Saxonian, the Polish and the Bohemian, which turned out to be one with more political weight from the 15th century onwards. A second college, the Academia Ferdinandea, was created in 1556 and was run by the Jesuits. It is better known by the name Klementinum. In 1654, Charles University and the Jesuit Clementinum were unified in a single institution, then called “Charles-Ferdinand university”. From that time until well into 19th century the university of Prague was organized in a traditional way, around four disciplines: philosophy, theology, law and medicine. The teaching of the first two, philosophy and theology, was a monopoly of the Jesuits at the Clementinum, while the superior faculties of law and medicine were lay faculties, controlled by the state.
Mathematics was taught at the faculty of philosophy, and since attending philosophy courses was compulsory for all students, the dissemination of mathematical sciences in Prague and Bohemia was monopolized by the Jesuit order for about two centuries, from the first half of the XVIIth to the disbanding of the order in 1773.
The place of mathematics in the Jesuit curriculum had been a hotly debated topic among Jesuit educators and reformers soon after the creation of the order. Eventually, Christophorus Clavius’ strenuous campaign to obtain a revered place for mathematics in the curriculum won: “owing almost entirely to his dogged and tireless leadership – A. Alexander recounts – only a few decades later, Jesuits were setting the standard for the study of mathematics in Europe.” And, within Europe, in Prague too.
But what did students learn when they studied maths under the Jesuits at the Clementinum? One thing that should be remarked is that the organization of the teaching kept pretty much stable until the dissolution of the order, and included, for example, disciplines we would not treat as part of mathematics today: civil and military architecture, optics (catoptrics and dioptrics), hydrostatics.
Before the Jesuits order was suppressed in the Habsburg empire in 1773-74, the system of university education had already undergone a gradual process of modernization and specialization through several reforms, starting from 1741. If we focus on the teaching of mathematical sciences, a significant change brought about by the reorganization of the curricula from the half of the 18th century was an emphasis on mathematics and physics. One of the main consequence of these reforms was that new chairs were introduced, and the teaching of disciplines which did not belong to the traditional Jesuit cursus was promoted. For instance, alongside the traditional chair of elementary mathematics, a chair of advanced mathematics (mathesis sublimior) was created in 1762. Concomitantly, the traditional Aristotelian framework which dominated the teaching of natural sciences was abandoned and substituted by an approach oriented towards experimental sciences.
Such reforms in the scientific education began, not without difficulties, under the leadership of the Jesuit Joseph Stepling (1716-1777), director of the philosophical faculty at Prague university from 1763 to 1776, and continued with his successor and most brilliant student, Jan Tessánek (1728-1788). Another important change was the introduction of the German as the official language for teaching in 1784, which opened the door to the circulation of German textbooks. Meanwhile, the modernization of technical higher education was prompted by the creation of a special chair of practical mathematics (1784), whose first professor was Franz A. L. Herget (1741-1800), followed by Joseph Havle (1763-1840) and A. Bittnar (1777-1844). Finally, the creation of a polytechnical school upon the model of the French Ecole polytechnique, in 1803, crowned the ongoing process of modernization in the 18th century Czech lands.
The table below summarizes the historical evolution in the teaching of mathematics between 1760 and the end of the 18th century. We note that the disbanding of the society of Jesus, although in some cases caused the removal of Jesuit professors from their chair, did not seem to have changed the structure of mathematical education, which continued to be part of the faculty of philosophy, except for an independent programme in advanced mathematics.
When Bernard Bolzano, a key figure in the history of mathematics, logic and philosophy, stepped into Prague university as a teenager, at the end of 18th century, the education system of the Jesuits was still in place in its general lines, even though the order was then gone for more than 20 years.
The disestablishment of an organization that had ruled for centuries was a process that affected the practical and intellectual aspects of the lives of the people involved. A paradigmatic change of sort, which has too often been neglected when studying the emergence of modern mathematics, such as in the case of Bolzano.
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