While you don't need any math to have an intuitive understanding of how steam engines work, you need to understand thermodynamics in order to engineer efficient engines, which is what happened in the latter part of the 19th century. The development of the science of thermodynamics was greatly stimulated by its applications, and vice-versa.
I imagine there is a similar story in chemical engineering.
I had an interesting realisation a year or two back: coal and petroleum each saw a major boom first in use-as-fuel, and then a secondary realisation of the chemical properties and utility of the substances. First coal-tar chemistry in the 1850s and 1860s (or thereabouts), then synthetics, in the 1920s and 1930s, mostly.
Virtually all modern synthetic plastics (urethane, polyethelyne, PVC, Nylon, etc.) were invented in the 1930s.
This also plays out in how eras appear to us. For clothing from -2 million bce - 1890, you had leather, cotton, flax, wool, silk, and fur, plus in areas woven grasses and other materials, with the plant fibres being vastly less expensive.
(Many of these were also fairly recent discoveries -- knitting, as an example, didn't exist until the Mediaeval period, and weaving progressed massively from ~1 AD through the 19th century).
In the 1890s, the first synthetic viscose came along (essentially rayon I believe). Then nylon and such in the 1930s, with the first synthetics. Even through the 1950s, virtually all high-fashion clothing was wool, silk, or fur, but the first synthetics, many in athletic or mountaineering wear, began to appear, with an explosion in the 1960s of synthetics and dyes, giving the characteristic look of the 1960s and 1970s.
There's been some walking back from all-synthetic-all-the-time, though they remain in high use.
Another thought is on the point you'd made: the interplay of steam power and thermodynamics, with engineering driving science through that period.
I imagine there is a similar story in chemical engineering.