Short answers, pulled from the story.
Filippo Brunelleschi is generally credited with developing a demonstrable system of linear perspective, conducting experiments between 1415 and 1420 that included drawings of Florentine buildings in correct perspective. Leon Battista Alberti then published the first written treatise on the method, De pictura, around 1435.
Around 1420, Brunelleschi painted the Florence Baptistery in perspective, drilled a hole in the back of the panel, and invited observers to look through it at the real building. He then held a mirror between the painting and the building so observers could compare the painted image directly to the actual structure. The original panel is lost.
De pictura, written by Leon Battista Alberti around 1435, was the first published treatise explaining how to represent depth correctly in painting. Alberti's breakthrough was framing perspective through planar projections and similar triangles rather than the conical geometry of the eye, making the mathematics accessible to practicing artists.
Chinese painters used oblique projection from at least the first or second century until the eighteenth century. The technique also appeared in Japanese art, including the Ukiyo-e paintings of Torii Kiyonaga, who lived from 1752 to 1815.
Zeeman's Paradox refers to the observation that viewers rarely notice the geometric distortions built into a perspective image even when they are not standing at the mathematically correct vantage point. In practice, the eye and brain compensate, making a mathematically imperfect view appear acceptable.
Piero della Francesca was the first to accurately draw the Platonic solids as they would appear in perspective, doing so in his De Prospectiva pingendi in the 1470s. He also extended Alberti's work by covering solids positioned anywhere in the picture plane, not just figures on the ground.