Mathematics is an abstract language created by humans, which interprets universal patterns. It started in the physical/visual world as a way to quantify things: land, livestock, building materials, etc. Through its abstraction and withdrawal from specific computations it evolved to stand on its own as mathematics for mathematics' sake.
I recently watched the four-part BBC documentary, The Story of Maths, presented by Oxford professor Marcus du Sautoy, who does a great job of crunching the history of math into four hours, while taking the viewer around the world.
I tuned into the series more as visual thinker than as a mathematician. It is easy enough to see how a quantity (of whatever) can be represented with symbols. Sautoy offers that even 0 as a symbol for nothing, a concept that eluded the early mathematicians including the Greeks and Chinese, may have come from the circular divet that was left in the earth when a counting stone was removed from its place.
What I found most interesting is that while some mathematics can be visualized, most situations are formalized through a formula. That is, except for perspective, whose solution was in the command of vanishing points. Of course there are numbers behind that system but it was a case of mathematics whose problem arose through two-dimensional representation of a three-dimensional world, but was solved through a purely mechanical act by artists.
Basic geometry is a very visual kind of math but the question is, which came first the shape or the possibility of the shape? With a set of numbers/coordinates I can generate a shape but I can also create a shape that calls into play a set of numbers. Are the geometric forms we observe and (re)create merely byproducts of these "numbers" or do the shapes create a case for the numbers? Or is it that they are one in the same - the same information that can be represented visually or numerically?
[image source: http://mathworld.wolfram.com/Perspective.html]
A working perspective was not developed until the early Renaissance and was hailed as a truth. Ironically, within a few hundred years it became reputed as a lie. It seems, however, that the trickery is in our skewed observation: our stereoscopic eyes and visually comprehensive minds create an illusion that is as false in reality as it is on a wall or a canvas.
In terms of art history it is interesting to note that the use of perspective was often not used merely to recreate an environment so much as it was a way to create a more believable world to tell a story, especially one that no one was still around to refute. Pictured above is Raphael's School of Athens, completed in 1511 to depict a hypothetical mashup of ancient philosophers.
I find that the most interesting use of perspective was by the surrealists, who did not abandon it during Cubism, Abstract and other movements, because it gave them the power to create a space for their strange worlds, as we see 420 years later with Salvador Dalí's The Persistence of Memory.
