As the impact of the American and French Revolutions was felt across Europe, a social atmosphere arose that encouraged ground breaking work in mathematics. Karl Gustav Jacob Jacobi, who attracted early attention from luminaries such as Adrien-Marie Legendre and Karl Gauss, appeared alongside and sometimes worked with a handful of innovative contemporaries like William Hamilton, Augustin-Louis Cauchy, Peter Dirichlet, and Niels Abel. Jacobi's own contributions range across older subjects in math such as number theoryand newer fields like analysis. Two mathematical terms he devised now bear Jacobi's name. He electrified the teaching profession with an unprecedented practice of opening up his theoretical notes to his students, thereby inventing the research seminar now common in universities. While the political instabilities of post-revolutionary times sometimes threatened Jacobi's livelihood, his sheer genius was always enough to attract a new protector to sponsor his continued work. Jacobi's mathematics had an immediate...