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

Alexander Marr's book is a recovery of a remarkable figure: Mutio Oddi of Urbino (1569-1639), architetto ducale, professore di matematica nelle Scuole Palatine, ingegnere della Serenissima Repubblica di Lucca - architect, mathematician, engineer, not to mention designer, geometer, collector, instrument broker, courtier, teacher, scholar and writer - and the author of treatises on surveying, measurement and gnomonics (the art of measuring time by the sundial) and a marvellous set of gheribizzi (fantasies or caprices) for the architectural redevelopment of Urbino.

He is positioned by Marr as a bridge between the artistic traditions represented by his great Urbinate predecessor, Raphael, and the scientific culture of his contemporary and foil, Galileo. There may be an element of symbolism in this bridge-building (or a rhetorical flourish), yet the connections are there to be made. Oddi trained first of all as a painter, apprenticed to the artist Federico Barocci; the apprenticeship was cut short when it was discovered that he suffered from defects in his vision.

This led him to abandon painting in favour of mathematics, but his interest in art ran deep. Late in life, he purchased and renovated the house in which Raphael had been born. When it came to a career, there were certain similarities between Oddi's and Galileo's: both were clients of the "Archimedes of Pesaro", Guidobaldo del Monte; both were mathematics teachers who invested heavily in instruments (compasses, mirrors, clocks, surveying instruments and the like); both were deeply involved in the culture of disegno (design). Unlike Galileo, however, Oddi had the misfortune never to achieve a major intellectual breakthrough. Despite his best efforts, therefore, he has slipped through the cracks of history, a footnote in every field.

Marr makes him whole. That is quite a feat, given the need to master so many trades, and also to reimagine what it meant exactly to be a practising mathematician - or "mathematical practitioner", as he prefers to say - in that time and place. This yields a compelling account of an extraordinarily rich mathematical culture. Perhaps the most impressive set piece is an extended analysis of a painting by the Milanese artist Daniele Crespi: a double portrait of the mathematician Oddi and the merchant Peter Linder engaged in a lesson about geometrical optics. The portrait depicts the two friends seated in the intimate space of the studiolo. Linder is studying a geometrical diagram; Oddi points to it, as if to explain. He is teaching, with the tools of the trade to hand - an inkwell, a mirror, a beam compass. For these men, mathematics was a sociable discipline. Mathematical practice was nothing if not civilised. The painting is a testament to friendship; the painter himself was Oddi's friend and former pupil.

This is a book much concerned with material culture. Appropriately enough, it is beautifully produced. Oddi himself would have been pleased with the lavishness of the design - there is no stinting on the paper, the illustrations, the apparatus - and he would surely have been curious about the mix of commerce and culture that has made it possible. "Published with the support of the Getty Foundation," it declares, while the author acknowledges his debt to the Carnegie Trust, the Scouloudi Foundation, the Frances Haskell Memorial Fund, the Max Planck Institute and the Leverhulme Trust, among others. Despite all the jive talk of interdisciplinarity, professional specialisation and intellectual fragmentation make it difficult for us to comprehend a life or a mind or a milieu like Oddi's. Between Getty and Carnegie, Marr has done us a service.