Nearly thirty years ago, as a green graduate student, I made earnest notes on Oronce Fine as I tried to explore the contours of the Renaissance mathematical arts. My guide at the time was Richard Ross's 1971 PhD on Fine and the articles that emerged from it. Ross put on a brave face but could not conceal the disappointment that lay behind his research. Despite his prolific publication record Fine clearly did not belong in the pantheon. Ross's verdict in a 1975 Isis article on Fine's trigonometric work was typical: ‘not only unoriginal; it was also behind the times’ (p. 385). In the professionalizing academic world of 1970s history of science, where the scientific revolution was key for both research and teaching, Ross's comment that Fine's work was nevertheless ‘still worthy of the respect and consideration of the historian of mathematics’ (p. 386) hardly served as an incendiary call to arms for those enthused by the history of ideas.

Alex Marr's volume provides a rich and refreshing index of the fruitful changes that the histories of science and mathematics have experienced over recent decades. Marr and his twelve authors no more establish Fine as a titan of the intellectual canon of Renaissance science or mathematics than did Ross. The point is that this is no longer the only game in town. Rather than the object of worthy but uninspiring attention, Fine comes into his own as an extraordinary cultural actor, redefining the possible roles and activities available for mathematics in Renaissance France.

After teaching in the colleges of Paris in the 1520s, Fine was appointed the first Royal lecturer in mathematics at the recently founded Collège Royal in 1531. From this pre-eminent and highly visible position Fine spent the rest of his life teaching and publishing in a broad range of the mathematical arts. While evidently working within the contemporary system of patronage, Fine's career and fortuna are inseparable from the realm of print: as editor, author, engraver and corrector for the press, he was part of a generation which saw dramatic possibilities for mathematics. Through finely composed and designed books, mathematics was promoted as polite and useful, as a subject fit to engage the curiosity, taste and administrative needs of bishops, nobles and councillors, as well as students and gentlemen.

Marr is to be congratulated for assembling a fine cast of contributors, most of whom spoke at the conference on Fine he organized in St Andrew's in 2006. Individual chapters study topics such as Fine's claims on the status of mathematics, his practical geometry, his theoretical and practical work in cartography, and his legacy – both his position in relation to the French algebraic tradition and his place within the often overlooked tradition of water clocks. There are two contributions on cosmography, reflecting the high significance of this topic in Renaissance mathematical teaching.

Invidious as it is to pick out individual essays in a balanced collection, I found especially stimulating Isabelle Pantin's institutional and intellectual setting of Fine, both in the context of the foundation of the Collège Royal and between Lefèvre d'Etaples and Ramus. Also impressive is Katherine Eagleton's demonstration of how Fine appropriated medieval textual traditions of sundials and transformed them in the new world of Renaissance print. Sven Dupré presents a careful analysis of Fine's work on burning mirrors, noting, like Eagleton, how Fine drew on medieval manuscript sources. Dupré also concludes that Fine's work was ‘practical mathematical and bookish rather than artisanal’ (p. 75), and Adam Mosley similarly tries to pin down the elusive character of Fine's endeavour in cosmography by referring to it as ‘theoretical practical mathematics’ (p. 129). Such nuanced characterizations reflect a deepening engagement with the diversity of mathematics in the period, and will surely provide the basis for further discussion. Henrique Leitão provides a sharply focused study of Pedro Nunes's reputation-establishing critique of Fine's efforts at circle-squaring, and the volume is rounded out by Stephen Clucas's reflective epilogue, which almost makes the job of the book reviewer redundant.

By featuring a collection based primarily on subject disciplines, the volume is bound to echo to some extent the historiography it seeks to replace. But the individual essays, and Marr's introduction, also suggest fresh avenues for future studies. Topics such as Fine's relations with his printers and publishers, and his work as illustrator, engraver and instrument-maker, seem ripe for further investigation. Fine may turn out to be most important for just those issues that are most difficult for us to access and recover. With a career focused on teaching, presentation, style and spectacle, Fine invites reflection on the difficult question of the nature of the public space that he inhabited – and indeed on the extent to which he helped to create a new kind of public space for mathematics. This volume certainly puts beyond doubt Fine's significance for the emergence of mathematics as culture – didactic, commercial, sociable, visual, ingenious and practical.