If Piero bore psychological consequences of his father's aggressive behaviours, they are not discernible to us today. The son did construct a life that replicated his father's behaviour of labouring to elevate himself from his modest beginnings.
Piero is important in the history of painting and mathematics because he strove to surpass customary conceptions of painting and to record his geometric and mathematical calculations. He was neither the product of his family ambience nor Florentine inventions in perspective and naturalistic depictions of the human body.
His cultural production has a curious dual nature of the traditional and the innovative. His meticulous scientific reconstructions of space and humans were often placed in traditional altarpieces. His writings on painting, mathematics, and geometry reveal a striving for meticulous precision and original constructions, but he betrays his modest origins in his use of the dialect of San Sepolcro and lack of elegance. Such a duality is not customarily a choice of the individual but a result of the circumstances of one's formation.