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

The Italian mathematician Matteo Oddi (1569-1639) was not one of the outstanding figures of his age, but his career offers an interesting view on mathematical life in the early seventeenth century. He made a promising start as court architect to the duke of Urbino, but later he fell from favor and had to spend nearly thirty years in exile, first in Milan, later in Lucca as master of fortifications. Only near the end of his life was he allowed to return home. As a result, Oddi was constantly moving between different worlds. Besides working as an architect and engineer, he gave mathematics lessons, wrote books, and acted as a middleman between Urbino's instrument makers and wealthy patrons. Forced to spend most of his career away from friends and relatives, he kept a busy correspondence. A thousand letters have been preserved, apart from drawings, notebooks, and other sources.

Drawing on this material, Alexander Marr aims to write "a holistic account of a late Renaissance life in mathematics and its materials" (p. 244, n. 42), but this description seems not quite adequate. His book does not offer a chronological or systematic overview. It is rather a volume of articles, each of which centers on some general theme as illustrated by Oddi's career. So, Oddi's trading in instruments, his teaching, and his book production are described as illustrating Renaissance friendship and the gift economy. His drawings are studied as a way of revealing the place of disegno in the mathematical arts.

A theme which recurs at several instances is the locality of knowledge. As a citizen of Urbino, Oddi was aware of standing in an illustrious tradition, notably represented by Commandino and Baldi, whose fame he promoted and whose approach he consciously continued. He also favored the Urbino style of mathematical instruments. All this does not add up to a full overview of Oddi's network or activities, although three appendixes partly make up for this. They list his pupils, the recipients of his second book, and the instruments he designed. The book is well produced and lavishly illustrated.

Marr's discussion is both guided by and limited to themes that are topical in modern history of science. He is certainly up to date with the relevant literature—and likes to show it. On 219 pages of text and illustrations, there are 73 pages of notes. Many of those are inessential, but hidden among them one may also find important qualifications which properly should have been in the text (e.g., p. 283, n. 90). As a result, closely following the argument requires something of an effort.

On finer scrutiny, flaws do appear: for example, when Marr discusses Oddi's attitude to Galileo and the Copernican system, the quotes he gives might support his argument (assuming that p. 309, n. 107 is a slip of the pen), but the context for them is given in such a vague way that a less charitable reader might well come to a completely opposite view. In another instance, Marr discusses at length the double portrait of Oddi giving a mathematics lesson to the German merchant Peter Linder. He interprets a diagram in the painting as representing reflection in a concave mirror (pp. 97-103). However, he only discusses elements which support his interpretation and glances over others. The curve in the diagram which appears to be emphasized by the painter (Oddi's index finger is next to it) is not even mentioned. Marr's interpretation is mainly based on the occurrence elsewhere in the painting of a concave mirror and a beam compass. One hundred pages later (p. 197) we are informed of the occurrence of the same two instruments in another painting connected to Linder (this time without optical diagram).

Oddi is certainly an interesting subject and, as Marr shows, he reflects many aspects of Renaissance culture. However, Marr appears more at...