When I think of linear algebra or calculus concepts, it always helps to visualize them as lines and planes. It's tough to imagine these concepts being discovered without such visualizations, although they are clearly man-made.
From The Visual Display of Quantitative Information by Edward R. Tufte, Page 28:
This reputed tenth- (or possibly eleventh-) century illustration of the inclinations of the planetary orbits as a function of time, apparently part of a text for monastery schools, is the oldest example of an attempt to show changing values graphically. It appears as a mysterious and isolated wonder in the history of data graphics, since the next extant graphic of a plotted time-series shows up some 800 years later.
Tufte himself was citing A Note on a Tenth Century Graph by H. Gray Funkhouser:
According to Funkhouser, the astronomical content is confused and there are difficulties in reconciling the graph and its accompanying text with the actual movements of the planets. Particularly disconcerting is the wavy path ascribed to the sun. An erasure and correction of a curve occur near the middle of the graph.
And in Page 29:
It was not until the late 1700s that time-series charts began to appear in scientific writings. This drawing of Johann Heinrich Lambert, one of a long series, shows the periodic variation in soil temperature in relation to the depth under the surface. The greater the depth, the greater the time-lag in temperature responsiveness. Modern graphic designs showing time-series periodicities differ little from those of Lambert, although the data bases are far larger.
The Cartesian coordinate system was developed by René Descartes in early 17th century, it is a powerful tool to link algebra to geometry.
The polar coordinate system was introduced in the same century too, Sir Isaac Newton was one of its early developers.
