University of Chicago Press

A forgotten episode of mathematical resistance reveals the rise of modern mathematics and its cornerstone, mathematical purity, as political phenomena.The nineteenth century opened with a major shift in European mathematics, and in the Kingdom of Naples, this occurred earlier than elsewhere. Between 1790 and 1830 its leading scientific institutions rejected as untrustworthy the “very modern mathematics” of French analysis and in its place consolidated, legitimated, and put to work a different mathematical culture. The Neapolitan mathematical resistance was a complete reorientation of mathematical practice. Over the unrestricted manipulation and application of algebraic algorithms, Neapolitan mathematicians called for a return to Greek-style geometry and the preeminence of pure mathematics.For all their apparent backwardness, Massimo Mazzotti explains, they were arguing for what would become crucial features of modern mathematics: its voluntary restriction through a new kind of rigor and discipline, and the complete disconnection of mathematical truth from the empirical world—in other words, its purity. The Neapolitans, Mazzotti argues, were reacting to the widespread use of mathematical analysis in social and political arguments: theirs was a reactionary mathematics that aimed to technically refute the revolutionary mathematics of the Jacobins. During the Restoration, the expert groups in the service of the modern administrative state reaffirmed the role of pure mathematics as the foundation of a newly rigorous mathematics, which was now conceived as a neutral tool for modernization. What Mazzotti’s penetrating history shows us in vivid detail is that producing mathematical knowledge was equally about producing certain forms of social, political, and economic order.

The landscapes of Madagascar have long delighted zoologists, who have discovered, in and among the island’s baobab trees and thickets, a dizzying array of animals, including something approaching one hundred species of lemur. Madagascar’s mammal fauna, for example, is far more diverse, and more endemic, than early explorers and naturalists ever dreamed of. But in the past 2,500 or so years—a period associated with natural climatic shifts and ecological change, as well as partially coinciding with the arrival of the island’s first human settlers—a considerable proportion of Madagascar’s forests have disappeared; and in the wake of this loss, a number of species unique to Madagascar have vanished forever into extinction.In Extinct Madagascar, noted scientists Steven M. Goodman and William L. Jungers explore the recent past of these land animal extinctions. Beginning with an introduction to the geologic and ecological history of Madagascar that provides context for the evolution, diversification, and, in some cases, rapid decline of the Malagasy fauna, Goodman and Jungers then seek to recapture these extinct mammals in their environs. Aided in their quest by artist Velizar Simeonovski’s beautiful and haunting digital paintings—images of both individual species and ecosystem assemblages reproduced here in full color—Goodman and Jungers reconstruct the lives of these lost animals and trace their relationships to those still living.Published in conjunction with an exhibition of Simeonovski’s artwork set to open at the Field Museum, Chicago, in the fall of 2014, Goodman and Jungers’s awe-inspiring book will serve not only as a sobering reminder of the very real threat of extinction, but also as a stunning tribute to Madagascar’s biodiversity and a catalyst for further research and conservation.

In mathematics, “buildings” are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas. Almost twenty years after its original publication, Mark Ronan’s Lectures on Buildings remains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field. Lectures on Buildings will find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups. “Ronan’s account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings.”—Bulletin of the London Mathematical Society