XIX Century — Math to everyone
We've seen that by XIX century, Math teaching became popular among schools and Universities. Analysis and Differential/Integral Calculus were getting fixed among Physics, Astronomy and other areas, generating studies on pure and applied mathematics. Atomic theory was getting solid basis, such as electromagnetism (with Faraday's works). Society finally had more access to science.
Among this scenario, we shall mention another important figure for mathematics — Augustin-Louis Cauchy (1789–1857), a French mathematician and engineer obsessed by rigorous mathematical proofs during his Professor career.
Cauchy gave base studies for the modern functions of complex variables, divergence and convergence of series, differential equations, probability and physics. The way you learn limits and derivatives (if you have learnt the into the traditional way) are possibly according to Cauchy's teaching proposal. Curiosity point: the term 'matrix determinant' was proposed by Cauchy.
Cauchy can be considered a pioneer into analysis field. As we will see in the next posts, he was also responsible for having Abel's and Galois' works forgotten for several years before Mathematical community recognised them as brilliant studies. Well, happens to all of us.
Last paragraph just for historical reflection: Catholic Church, responsible for several atrocities against those who want to develop scientific knowledge, was opening its mind by XIX Century also. As an example, we can mention the figure Bernard Bolzano (1781–1848), a priest who later became a mathematician (in simple terms, his works consisted in applying arithmetic techniques into analysis).