The book is an excellent work on the history of national and international mathematical communities and on the process of its internationalization in the period between 1800 and 1945. The book is divided into 18 chapters written by 20 authors (T. Archibald, E. Ausejo, J. E. Barrow-Green, A. Brigaglia, J. W. Dauben, S. E. Despeaux, D. D. Fenster, H. Gispert, I. Grattan-Guinness, J. J. Gray, M. Hormigón, O. Lehto, J. Lützen, L. Martini, K. H. Parshall, A. C. Rice, Ch. Sasaki, S. L. Segal, R. Siegmund-Schultze and Y. Xu). Each chapter describes the evolution of mathematical communities, research and education trends in relation to the political and economical situation in Europe (France, Britain, German, Italy, Spain) and in America and Asia (China and Japan). Special attention is paid to the American, Chinese and Japanese mathematical communities as well as to the situation in German after 1933. The book describes the role of the most important European mathematicians (including Ch. Hermite, G. Mittag-Leffler, C. Arzelà, L. Dickson), the significance of the most important European mathematical journals (for example, Journal de mathématiques pures et appliquées, Acta Mathematica), the creation of national mathematical societies (e.g., Société mathématique de France, Circolo mathematico di Palermo), the development towards the creation of the international congress of mathematicians and the establishment of the International Mathematical Union. A lot of references to published as well as unpublished sources and many historical and bibliographical notes appear in each chapter; hence the book can influence future investigations of interesting historical questions connected with the internationalization of research-level mathematics. The book can be recommended not only to historians of mathematics but also to professional mathematicians, teachers and students who want to understand the creation of international mathematics

Reviewer:

mnem