Lützen, Jesper Joseph Liouville, 1809–1882: master of pure and applied mathematics. (English) Zbl 0701.01015 Studies in the History of Mathematics and Physical Sciences, 15. New York etc.: Springer-Verlag. xix, 884 p. DM 228.00 (1990). Joseph Liouville was a French mathematician in the generation between Galois and Hermite. In this book, the author discusses Liouville’s scientific career: his education and his work as a teacher, journal editor, politician and academician. This book is mainly divided into two parts. The first part contains a chronological account of Liouville’s career, Liouville’s mathematical and physical works also have a central place in the first part. This part is divided into six chapters viz. (1) Youth (1809–1830), (2) Climbing the academic ladder (1830–1840), (3) Professor, (4) Academician and editor (1840–1848), (e) The Second Republic (1848–1852), (5) The last flash of genius (1852–1862), (6) Old age (1862–1882). In the second part, we find a more thorough analysis of various aspects of Liouville’s work. It is divided into ten chapters concentrating on different mathematical and physical fields of which chapters 10 and 11 are slightly revised versions of two previously published papers. The chapters are under the following headings: (7) Juvenile work, (8) Differentiation of arbitrary order, (9) Integration in finite terms, (10) Sturm Liouville theory, (11) Figures of equilibrium of a rotating mass of fluid, (12) Transcendental numbers, (13) Doubly periodic functions, (14) Galois theory, (15) Potential theory, (16) Mechanics, (17) Geometry. Besides these chapters, there are three appendices under the following headings: Appendix I – Liouville on Ampère’s force law, Appendix 2 – Liouville’s notes on Galois theory, Appendix 3 – The sketch of contents of Liouville’s course on rational mechanics at the Faculté des Sciences (1864–1865). There is a note in each chapter (except chapters 1, XII–XV, XVII) which is to be considered as a valuable addition. A bibliography is given at the end of the book which contains (i) unpublished manuscripts and other archival material, (ii) List of J. Liouville’s published works, (iii) Other references. If we analyze then we say – Liouville’s production is characterized by a slow movement from applied to pure mathematics. The author tries to write the first part in a narrative style whereas the second part is more discursive. The book is written scholarly and will be helpful for those who study the history of modern mathematics. Reviewer: P.K.Majumdar Cited in 4 ReviewsCited in 28 Documents MSC: 01A70 Biographies, obituaries, personalia, bibliographies 01A55 History of mathematics in the 19th century Keywords:celestial mechanics; differential equation; electro-dynamics; higher order equation; integration in finite terms; rational mechanics; Sturm-Liouville theory; transcendental numbers; doubly periodic functions; Galois theory; potential theory Biographic References: Liouville, Joseph PDFBibTeX XMLCite \textit{J. Lützen}, Joseph Liouville, 1809--1882: master of pure and applied mathematics. New York etc.: Springer-Verlag (1990; Zbl 0701.01015)