>Alberti invented the theory of perspective, designed
>important buildings, etc.
"Invented" gives him a little too much credit I think. Brunelleschi, to whom Alberti's book "On Painting" is dedicated, came up with the vanishing point and there were many other contributors whose work Alberti codified in "On Painting". A book by an art historian named Edgerton traces development of perspective in Europe back to beginnings in Giotto. Edgerton argues it was a rediscovery of techniques known to ancient painters. He makes a compelling argument that perspective was central to the development of modern European thought and ties it in with optics, math, and theology, particularly the association of God and creation with light.
Carlo Ginzburg has a nice article about a Jesuit in Canada writing an account of an Indian who is asked "what happened to your people." The Indian says the problem is "all these lines you are drawing on the earth." Ginzburg notes that the answer sounds crazy but is close to the truth because maps, drawn using rules of perspective, were crucial to Europeans in conquering the whole wide world.