The decorative program of the Gubbio studiolo signifies the pursuit of humanist interests and virtues. This is further emphasized by the inscription in the frieze that runs along all sides of the room. Its Latin text reads: "See how the eternal students of the venerable mother, men exalted in learning and in genius, fall forward, supplicantly with bared neck and flexed knee, before the face of their parent. Their reverend piety prevails over justice and none repents for having yielded to his foster mother." Federico's high regard for the liberal arts, especially mathematics and geometry, is well known. He was also passionate about architecture and wrote that mathematics and geometry, being based on scientific truth, are "the most important of the Liberal Arts, as well as the very foundation of architecture." This statement is key to our understanding of the spirit of "mathematical humanism" that is reflected in the details of the decoration of the Gubbio studiolo.

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