In the folklore of mathematics, James Joseph Sylvester (1814-1897) is the eccentric, hot-tempered, sword-cane-wielding, nineteenth-century British Jew who, together with the taciturn Arthur Cayley, developed a theory and language of invariants that then died spectacularly in the 1890s as a result of David Hilbert's groundbreaking, `modern' techniques. This, like all folklore, has some grounding in fact but owes much to fiction. The present volume brings together for the first time 140 letters from Sylvester's correspondence in an effort to establish the true picture. It reveals - through the letters as well as through the detailed mathematical and historical commentary accompanying them - Sylvester the friend, man of principle, mathematician, poet, professor, scientific activist, social observer, traveller. It also provides a detailed look at Sylvester's thoughts and thought processes as it shows him acting in both personal and professional spheres over the course of his eighty-two year life. The Sylvester who emerges from this analysis - unlike the Sylvester of the folkloric caricature - offers deep insight into the development of the technical and social structures of mathematics.

Karen Hunger Parshall is Professor of History and Mathematics at the University of Virginia. Her research focuses on the life, times, and mathematical work of James Joseph Sylvester.

• 1: Negotiating 'the world's slippery path'
• 2: Laying the foundation of a theory of invariants
• 3: Battling the authorities and the muses
• 4: Ending and beginning a career
• 5: 'Moulding the mathematical education of 55 million' Americans
• 6: Returning home