Postscript

As long as Algebra and Geometry have been separated, their progress has been slow and their usages limited; but when these two sciences were reunited, they lent each other mutual strength and walked together with a rapid step towards perfection.

Count Joseph-Louis de Lagrange (1795)

We know that Descartes’ fusion of algebra and geometry proved no less fruitful for one of these sciences than for the other. For, while on the one hand, geometers learned, through contact with analysis, to give their research a previously unknown generality, analysts, for their part, found powerful help in the images of geometry, both to discover their theorems and to state them in a simple and striking form.

Camille Jordan, Essai sur la géométrie à \(n\) dimensions, 1875.

This paper introduced the notion of angles between flats, which is equivalent to the statistical technique of Canonical Correlation Analysis.