Karen Parshall talks about the nineteenth-century mathematician James Joseph Sylvester. We learn about: Sylvester's family background and Jewish heritage (at time 0:27) being a Jew in Victorian Britain (1:21) his mathematical education (1:57) further impact of his Jewishness (2:37) a Jew at Cambridge (3:13) his first publications (4:24) progressing his career, and facing obstacles (5:25) end of his first stay in the USA (6:51) back in London: a job as actuary, and research progress (7:21) "creating his own mathematical community" (8:41) his friendship with Cayley (8:58) Invariant Theory (9:41) taking a degree in law (10:19) back to Academia as Professor of Mathematics at the Royal Military Academy, Woolwich (10:41) defining the "professional mathematician" (11:11) Sylvester at Woolwich (11:42) enforced retirement, establishing an international reputation (12:30) flourishing back in America as a research professor (13:37) return to England and the Savilian Chair at Oxford (15:46) More information, worksheets and other resources for the undergraduate mathematics curriculum: www.beingamathematician.org