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Joseph Liouville was the most important French mathematician in the gen eration between Galois and Hermite. This is reflected in the fact that even today all mathematicians know at least one of the more than six theorems named after him and regularly study Liouville's Journal, as the Journal de Mathematiques pures et appliquees is usually nicknamed after its creator. However, few mathematicians are aware of the astonishing variety of Liou ville's contributions to almost all areas of pure and applied mathematics. The reason is that these contributions have not been studied in their histor ical context. In the Dictionary of Scientific Biography 1973, Taton [1973] gave a rather sad but also true picture of the Liouville studies carried out up to that date: The few articles devoted to Liouville contain little biographical data. Thus the principal stages of his life must be reconstructed on the ba sis of original documentation. There is no exhausti ve list of Liou ville's works, which are dispersed in some 400 publications .... His work as a whole has been treated in only two original studies of limited scope those of G. Chrystal and G. Loria. Since this was written, the situation has improved somewhat through the publications of Peiffer, Edwards, Neuenschwander, and myself. Moreover, C. Houzel and I have planned on publishing Liouville's collected works.
List of contents
I. The Career of a Mathematician.- I. Youth (1809-1830).- II. Climbing the Academic Ladder (1830-1840).- III. Professor, Academician, and Editor (1840-1848).- IV. The Second Republic (1848-1852).- V. The Last Flash of Genius (1852-1862).- VI. Old Age (1862-1882).- II. Mathematical Work.- VII. Juvenile Work.- VIII. Differentiation of Arbitrary Order.- IX. Integration in Finite Terms.- X. Sturm-Liouville Theory.- XI. Figures of Equilibrium of a Rotating Mass of Fluid.- XII. Transcendental Numbers.- XIII. Doubly Periodic Functions.- XIV. Galois Theory.- XV. Potential Theory.- XVI. Mechanics.- XVII. Geometry.- Appendix I. Liouville on Ampère's Force Law.- Appendix II. Liouville's Notes on Galois Theory.- Notes.- Unpublished Manuscripts and Other Archival Material.- List of J. Liouville's Published Works.- Other References.
