When and where was first mathematical system of perspective in painting developed?

Answer 1

In ancient Greece, starting around 400 BC

Answer 2

Perspective painting is a way to make a 2-dimensional picture seem 3-dimensional. (This is also what a photo does.) As early as in paintings during the Roman Empire we find that artists were trying to achieve this. The definitive breakthrough came in the early 15th century by Brunelleschi and Alberti.

Answer 3

There are earlier signs of it, but as we know it, perspective originated from Greek and Roman architecture in the renascence because of the straight lines buildings have. An artist and architect, Filippo Brunelleschi, made a series of investigations that gave the foundations of later perspective. Piero della Francesca wrote a book that became the base to perspective theory. From there it's a matter of physics and lenses science.