It seems that every wants proof of something: a slick looking map, or statistics and bar graphs to prove certain things, like climate change. It seems like we've turned away from cultures that wouldn't have let industrial society happen in the first place. Does philosophy have any role to play today, or are people only able to be convinced if you show them the pie chart to back up what you're saying?
"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."
Roger Bacon, in Opus Majus, 1267.
So already in the late middle ages does the idea that mathematics is the basis of all knowledge arise. In the renaissance does it prosper in the thinking of people like Galileo and Kepler, who see the world of physics more in mathematical terms than people before them, and actually find mathematical formulas to describe it. People like Leibniz, Newton and Descartes definitely furthered this idea.
As to the visual presentation of mathematics, rather than in text, an important promotor of this was Florence Nightingale. She found a lot of difficulty in persuading doctors and administrators that hygiene in hospitals was important. She invented or at least popularized the pie chart to make people really concious of the impact of in-hospital infections.
Another aspect of your question is when people moved from "myths and traditional knowledge". I'm not completely sure what you mean by that, but I suppose it refers to oral traditions. Their fading away came with the written and printed word, long before mathematics came to be commonly seen as the cornerstone of certainty.