HERMIONE GIFFARD, MAKING JET ENGINES IN WORLD WAR II: BRITAIN, GERMANY, AND THE UNITED STATES. CHICAGO: THE UNIVERSITY OF CHICAGO PRESS, 2016. PP. 349. ISBN 978-0-226-38859-5.

Advances in mathematics originated in the war efforts to break encryption, optimize logistics or process and manage information. The impact of the Great War on such ‘internal’ aspects in mathematics is less obvious, but, repeatedly, the chapters emphasize the operation of artillery as a military and scientific problem. During the war, mathematicians played roles in enabling the technological advances of sound ranging, aeronautics and ballistics since these were known to depend on mathematical and computational skills, as well as on technological innovation, for improvement. Therefore the proving grounds at Gâvre in France, at the Anti-aircraft Experimental Section in Britain at Aberdeen, and the Ordnance Department in the United States became venues where different perspectives on mathematics met: military and academic, technological and more scientific, national and international.

Chapters by Aubin on Gâvre; Tom Archibald, Della Dumbaugh and Deborah Kent on the United States; and Barrow-Green on Britain each situate these meetings and conflicts in their local contexts, introducing a fascinating range of individual careers to make a general claim: considerable mathematical research – in an extended, non-academic setting – emerged from the technological, military challenges of precisely firing artillery on targets that were either moving or out of sight. Moreover, these military institutions also became hybrids where knowledge and relations were built that would later shape the academic milieu in the Allied countries. Key players of post-war academia, such as Oswald Veblen, would have formative experiences and build networks through the war effort. Thus the volume presents a wealth of information and perspectives on a topic that has received little attention in the history of mathematics but which can – and will – be of great interest not only to historians of mathematics, but also to historians of science more generally. It shows how structural grounds for comparison can emerge from careful case studies, of which more have subsequently been published from the research project. For good reasons of focus and delineation, the present emphasis is on the Allied side, but more research should benefit from even more explicit comparative analyses of the material presented here, from comparison with similar analyses of the Axis powers, and from integrating even more with existing research into issues such as the internationalization of mathematics and the institution-building efforts of the post-war period. The chapters are comprehensive, expertly researched and clearly presented. They make available in the English language existing, vernacular knowledge and new archival research by leading experts who contextualize developments in both local and thematic contexts. The volume is enriched by well-curated photographs and quotations, which help authentically situate mathematics within the catastrophe of the Great War. It is strongly recommended to all historians of science in the twentieth century.