## James Joseph Sylvester: Life and Work in LettersIn 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. |

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Academic Algebra American Journal American Mathematical Arthur Cayley Baltimore binary form Bodichon British calculation Calculus of Forms Cayley's Charles Charles Hermite coefficients Coit Gihnan Papers commentary to Sylvester's Comptes rendus correspondence covariants Daniel Coit Dear Cayley dear Sir degree Eisenhower Library equations evectant function Geometry George Gilman given Gordan Henry Hirst invariant theory J. J. Sylvester James Joseph Sylvester Johns Hopkins University Journal of Mathematics Karen Hunger Parshall Klein lectures letter to Cayley letter to Gihnan letter to Sylvester London Mathematical Society mathematician Mathematik matrix method minimum generating set noted Oxford Papers AC partition Paul Gordan Peirce Philosophical Magazine previous letter Professor professorship proof Quantics recall the commentary reciprocants result Rogal Society Sahnon Sciences Society of London Spottiswoode St John's College Sturm's Sturm's theorem Sylvester Papers Sylvester to Arthur Sylvester's letter theorem truly J. J. Sylvester Trustees University Press variables vols William Woolwich York