I just flipped back and forth between reading about 18th and 19th century developments in mathematics (analysis in particular) and 18th and 19th century transitions in art. The language of art history and the language of math history is very different. It does feel a little like going from color to black and white, or from something sunny, to something just starkly lit. But because so much of my recent reading has included the phrase modern mathematics, I couldn’t help but spend some time thinking about what people say about modern art.
What I find common to both are thoughtful shifts in the human questions: What’s really there? How can we talk about it? How can we express it?
For the sake of simplicity I’ll refer only to Paul Cezanne whose work is often thought of as the bridge between impressionist painting and modern art. Impressionist painting seems most centered on how we see, how our visual experience changes continuously, in time, with light. Cezanne, however, also took note of the geometric forms of nature, and further explored the effects of binocular vision, wanting to capture, if one could, the truth of his perception.
Painting must be motivated, to some extent, by a desire to reveal something about what is contained in what we see. And, while I’m taking a big leap here, mathematics can be said to be the exploration of what is contained in the whole of what we see and what we can subsequently imagine. As it is characterized by precision, a good deal of strictly thoughtful analysis must be assumed.
While mathematics can only be known with symbolic representation, its roots are in experience. It manages to extract forms and generalities from sensation and then it explores the value and significance of those forms. The transition to what we call modern mathematics can be seen as a shift away from continuing to play with the observations made (with respect to things like functions, limits, derivatives and integrals, series, alternative geometries) toward finding the simplest generalities that successfully characterize these things – essentially pinning down their truth. It required a new detachment, not unlike the modern artist, in order to find the forms rather than all of the examples of the forms. (I will write more specifically about some of these changes in another post).
For now I would like to quote Cezanne:
“May I repeat what I told you here: treat nature by means of the cylinder, the sphere, the cone, everything brought into proper perspective so that each side of an object or a plane is directed towards a central point. Lines parallel to the horizon give breadth… lines perpendicular to this horizon give depth. But nature for us men is more depth than surface, whence the need to introduce into our light vibrations, represented by the reds and yellows, a sufficient amount of blueness to give the feel of air.”
Recent Comments