The sole surviving piece of textual evidence that sheds light on the Linder gallery interior is a letter, sent on 28 March 1629, from the architect-engineer Giovanni Battista Caravaggio to his former tutor in mathematics, Mutio Oddi of Urbino. In the letter, Caravaggio (then in Milan) mentions a visit to their friend Pieter Linder, a German merchant who had also studied mathematics with Oddi, and who was the Urbinate scholar’s closest friend. He describes seeing, in Linder’s study, a painting showing a picture gallery in perspective, which is undoubtedly the Linder gallery interior. He then goes on to state that the invenzione (the subject matter) was ‘in large part’ due to Oddi, whose portrait medal is clearly visible on the central, octagonal table. Evidently, Oddi (presumably with input from Linder) orchestrated the picture’s content, transforming a relatively conventional, sketched proposal for the painting (now in the Royal Collection, Windsor Castle) into an elaborate allegory of the relationship between mathematics and disegno, of his friendship with Linder, and of their attitude towards cosmology. In the Linder gallery interior, Oddi presents disegno as a mathematical art, which is based on measurement and calculation – a position that is entirely consistent with the ‘Urbino school’ of mathematicians, to which he belonged. Like other members of this school, such as his own master, Guidobaldo del Monte, Oddi’s approach to cosmology was essentially conservative. Thus, while the ‘motto’ of the painting – Aly et alia vident – may be a plea for toleration in debates about the cosmic systems, we should be alert to its more caustic understones. In his published works, Oddi argued forcefully that the correct way of measuring the heavens was through traditional instruments, such as those scattered on the octagonal table of the painting. Indeed, it is notable that the telescope is conspicuous by its absence from this work, when it is present in other examples of the ‘pictures of collections’ genre. ‘Others may indeed’, Oddi suggests with a note of disdain, ‘see the heavens yet otherwise’, but the way to treat the problem of conflicting cosmic systems was not through the fallible sensory data provided by optical instruments (which relied, as he knew from his experience with mirrors, on an imperfect technology that resulted in imprecise devices), but instead through the certainty that resulted from geometry and with instruments that rest, just as the arts rest on disegno, upon its secure foundations. The books by Kepler on the octagonal table emphasize this point of view, for both (and especially the Tabulae Rudolphinae, which was based on Tycho Brahe’s measurements using traditional instruments) are about geometrical cosmology. Unfortunately, none of Oddi’s or Linder’s correspondence mentions Kepler (so the emphasis we should place on the Imperial Mathematician’s literary presence in the painting must remain speculative), but it is highly likely that both men were sympathetic to his work.