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Between Raphael and Galileo: Mutio Oddi and the Mathematical Culture of Late Renaissance Italy

Alexander Marr
University of Chicago Press
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Hardy Grant
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Alexander Marr’s book successfully intertwines two distinct though related themes. The subtitle gives the clue: we have here both a biography of an obscure but interesting Renaissance figure, and the light that his story throws on the social and cultural backdrop of his vibrant age.

It is just Muito Oddi’s ordinariness, Marr says (p. 9), that makes him so valuable as a witness. Excessive scholarly focus on giants like Galileo, he urges, distorts the historical record in several ways. It overemphasizes “pivotal moments”, it envelops the geniuses in “polemics and partiality” (p. 244), and it unduly marginalizes the contributions of lesser lights. Oddi’s well attested involvement in a wide spectrum of the contemporary scene offers, in Marr’s view, a useful corrective.

Oddi’s life was not without adventure. In 1601, aged thirty-two, he went into hiding in Venice after rashly wounding a secretary of the Duke of his native Urbino over a point of honor. Three years later a murky chain of events landed him in prison — where he wrote publishable treatises with ink and paper made from available scraps. Released in 1610, but condemned like Dante to a bitter exile from a beloved home, he earned his bread in Milan, where he taught mathematics, and in Lucca, where he grew rich designing fortifications. Allowed at last to return to Urbino, he bought, renovated, and eventually (1639) died in the “Casa Santi” in which Raphael was born in 1483.

His absence from histories of mathematics is not an injustice. He contributed to the subject nothing original. His knowledge of geometry, especially Euclid, was deep, but on his own admission he gave little study to algebra. But mathematics was for him only part of a formidable range of professional activity; Marr decides (p. 16) that the best label to put on him is “mathematical practitioner”. His four books were all devoted to mathematical instruments, in the sale of which he served as consultant and broker. On construction projects he functioned variously as surveyor, draftsman, builder of models, and site supervisor. Though hampered as an artist by defective vision, he “drew more or less every day, as architect and mathematician” (p. 179), he designed ornamental sculptures, and he was active in the art trade, as a collector and a go-between. This was a career which invites the cliché of “Renaissance” versatility.

His teaching reflected that diversity. Formally and informally, he imparted mathematics that ranged from rudimentary arithmetic to advanced geometry; but also he taught architecture to stonecutters, perspective to painters, the use of instruments to military engineers. At one time he held a chair of mathematics in Milan, which required two (!) lectures per week; but in addition he tutored the social elite at courts, and individuals in their homes. He was not above shaping his instruction to his own wider purposes, for example by stimulating interest in the instruments that he happened to be selling (p. 74).

Through such teaching, by Oddi and many others, mathematics enjoyed in late-Renaissance Italy a considerable expansion of participation and prestige. Specifically, Marr asserts (p. 116), its “fussy” and “abstract” aura was countered by demonstrations of its useful and sensually appealing “material associations”, above all through the growing popularity of instruments. Its image thus transformed, mathematics won a larger place in humanist education; it figured in the professional training of painters and of military engineers; and it played a role in the social polishing of young gentlemen. Wisely, Marr does not try to see in this ambience the source of technical progress in mathematics: the wellsprings of the period’s seminal advances — think Cardano, Bombelli, Viète — were largely internal.

Two dominant preoccupations gave coherence to Oddi’s many enterprises. On the one hand they were “bound together”, in his own mind, “by their common reliance on — or relationship to — geometry” (p. 167). The second of his foci was subtler. At the “very heart of [his] world”, Marr says (p. 21), was disegno, a complex and slippery concept which sixteenth-century elaborations had taken far from its root sense of “drawing”. Thus, for example, to Giorgio Vasari, the still famous teller of artists’ tales, disegno came to signify the theory of art and of design, and also the relation of theory to execution, for (he wrote) “it is a visible expression and declaration of the concept that is in the soul” (p. 214) — a view that Muito Oddi endorsed.

These twin foundations, geometry and disegno, stemming respectively from science and from art, ensured — and this is the core of Marr’s message — that many of Oddi’s activities forged links, mediations, between worlds: between mathematics and material culture, mind and hand, theory and practice. The bridges thus built had many dimensions: intellectual, social, cultural, commercial. The communities and networks created in this way spanned diverse subsets of the populace, and Marr is very good on their dynamics: perceptions of hierarchy, cultivation of patronage, the demands of etiquette, the elaborate rules and conventions of friendship (amicizia). Oddi’s dealings in the marketplace, as a middleman in the art world and in the instrument trade, and as a writer negotiating with publishers, add fascinating glimpses of the economic underpinnings.

One aspect of the bridges that practitioners such as Oddi helped to build has had, in many later eyes, especially profound significance. The “rapidly increasing proximity” (p. 93) of mathematical reasoning and hands-on experience of the physical world, the closer contacts of study and workshop, have been widely touted as key factors in the notoriously complex beginnings of the Scientific Revolution. Marr participates usefully in that ongoing debate by urging and documenting the modest but valuable contribution of toilers like Oddi, “whose significance consists not in major discoveries but in their roles as supporters, facilitators, brokers, disseminators, consumers and users of scientific knowledge” (p. 10).

This picture of “how specific social contexts could shape science” (p. 23) is compelling, but perhaps some readers will feel that in one important respect it overreaches. Marr says (p. 48) that Oddi, despite so often straddling mathematical and material cultures, never managed, like Galileo and Stevin (Marr’s examples) to bring these realms together “in novel ways to make original kinds of knowledge” (italics in original), and he ascribes this failure “largely” to Oddi’s conservative devotion to the mathematical heroes and traditions of his native town. But this is surely to overlook another, deeper cause: he lacked utterly the enabling gift of creativity. With all due allowance for the crucially transforming cultural currents that Marr so well describes, Galileo evokes “polemics and partiality” in historians precisely because his achievement was singular, and remains mysterious.

This is a splendid book. Alexander Marr, who teaches art history at the University of Southern California, has made excellent use of Oddi’s copious surviving legacy — including for example more than a thousand letters, detailed records of his teaching, several hundred drawings, the distribution list of one of his books; his handling of these primary materials, and his scholarship in general, are superb. His writing lapses only rarely and slightly from high standards. Rich in small details and in large perspectives, eminently readable and constantly enlightening, graced by eighty-two beautiful and varied illustrations, this lively account of a worthy man and a pivotal age deserves a wide audience.

Hardy Grant ( retired a number of years ago from the mathematics department at York University, Toronto, where his specialty was an undergraduate Humanities course on the cultural career of (Western) mathematics.