Mathematics past and present
In the early 18th century a struggle was still going on between the old and the new mathematicians. There was algebra, there was geometry and arithmetic. Many mathematicians fully believed that the ancient Greek mathematicians had kept their knowledge of algebra secret, that is, that they had used algebra to demonstrate the geometric theorems that we find in Euclid's Elements, the most important of the classic works. The algebra we recognize today was devised in the 17thcentury by Descartes. There were precursors, especially during the 16th century, but in 4th-century B.C. Greece there was no algebra.
When mathematics was taught at universities, including Uppsala, around 1700 it comprised much more than algebra, geometry, and arithmetic. It covered applications for the science of fortification, astronomy, optics, mechanics, geography, and even pyrotechnics. On the other hand, it was extremely rare for Newton's and Leibniz' theories to be taught. Nor were they understood.