The use of perspective in the visual arts—that is, the application of optical knowledge to convey a sense of depth in flat pictures or of increased depth in low relief sculpture, seems to resemble other craft practices. Perspective becomes a pragmatic matter, secondary to the main purpose of the work of art, providing a subset of the tools available for pursuing the greater, more significant purpose of producing a painting or sculpture that conveys an appropriate message with appropriate force and in an appropriately impressive manner. The emphasis some historians—of art and of science—have given to the introduction of new mathematical construction techniques tends to obscure this craft element, craft being characterized by continuity whereas historians of, say, the art of the fifteenth century tend to be interested in evidence of change. Accordingly, it is of interest that the same largely non-mathematical methods of constructing and organizing pictures and their sense of the third dimension that we find in the works of almost all Renaissance painters are also to be found in the work of one painter who we know could, and on occasion did, get the mathematical construction right, namely Piero della Francesca. Piero's treatise on perspective construction, De prospectiva pingendi (undated, but probably completed after 1460), was the model for all subsequent treatises on the subject addressed to painters, and the source of almost all these treatises’ worked examples, examples which themselves account for the bulk of their content. This Working Group paper examined Piero's pictorial choices and the nature of his compromises with the rules that his own treatise had laid down with perfect mathematical rigor. Even in the work of a highly competent mathematician, we do not see the introduction of a mathematization of space—indeed the notion of "space" as an entity in itself is anachronistic—but rather the use of a series of compromises in which art disguises art. Piero the mathematician knew the importance of rigour, Piero the painter gave precedence to the art of painting.