Mathematics past and present

In the early 18^th 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 Elementa, the most important of the classic works. The algebra we recognize today was devised in the 17^thcentury by Descartes. There were precursors, especially during the 16^th century, but in 4^th-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.

Follow the advancements in mathematics from Euclid to Euler:

Front page in the book Cursus sen mundus mathematicus, from the 1700s — Cursus seu mundus mathematicus – The Course or Universal Mathematics.
There were four equally large textbooks comprising a total of several thousand
pages. It was used at Uppsala and elsewhere in the early 1700s. (To get an
idea of the size, note the match lying on top of the book.) Only the professor
owned the book. Students had to copy it.
Photo: Staffan Rodhe. From the collections of Institut Mittag-Leffler.