Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi was born on 10 December 1804 in Potsdam, Kingdom of Prussia. He was the second of four children of banker Simon Jacobi and his wife Regina Leibmann Jacobi. His elder brother Moritz von Jacobi would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc. As a result of the good education he had received from his uncle, as well as his own remarkable abilities, after less than half a year Jacobi was moved to the senior year despite his young age. However, as the University would not accept students younger than 16 years old, he had to remain in the senior class until 1821. He used this time to advance his knowledge, showing interest in all subjects, including Latin, Greek, philology, history and mathematics. During this period he also made his first attempts at research, trying to solve the quintic equation by radicals¹. In 1821 Jacobi went to study at Berlin University, where he initially divided his attention between his passions for philology and mathematics. In philology he participated in the seminars of Böckh, drawing the professor's attention with his talent. Jacobi did not follow a lot of mathematics classes at the time, finding the level of mathematics taught at Berlin University too elementary. He continued instead with his private study of the more advanced works of Euler, Lagrange and Laplace. By 1823 he understood that he needed to make a decision between his competing interests and chose to devote all his attention to mathematics¹. In 1825 he obtained his doctorate from Berlin University with a dissertation on fractional calculus titled Disquisitiones Analyticae de Fractionibus Simplicibus. His doctoral advisor was Enno Dirksen. In 1826 he became a lecturer at Berlin University and in 1829 he was appointed professor of mathematics at Königsberg University. There he established a school of mathematics and attracted many talented students such as Paul Gordan, Otto Hesse and Friedrich Julius Richelot. He also collaborated with other eminent mathematicians such as Niels Henrik Abel (with whom he founded the theory of elliptic functions), Carl Friedrich Gauss (who praised him as "the greatest mathematician since Gauss"), Peter Gustav Lejeune Dirichlet (who succeeded him at Berlin University) and Bernhard Riemann (who extended some of his results on complex analysis)¹. Jacobi made significant contributions to various branches of mathematics such as analysis (especially elliptic functions and theta functions), algebra (especially determinants and matrices), number theory (especially quadratic forms and modular forms), differential equations (especially partial differential equations and variational calculus), mechanics (especially celestial mechanics and rigid body dynamics) and geometry (especially differential geometry and projective geometry). He introduced many important concepts and notations that are still widely used today such as the Jacobian matrix and determinant (which measure the local change of variables in multivariate functions), the Jacobi symbol (which generalizes the Legendre symbol for any odd modulus), the Jacobi ellipsoid (which is the shape of a rotating fluid mass in equilibrium), the Jacobi polynomials (which are orthogonal polynomials that arise in the expansion of hypergeometric functions), the Jacobi transform (which is a generalization of the Fourier transform for Jacobi functions), the Jacobi identity (which is a property of Lie algebras and Lie brackets), the Jacobi operator (which is a second-order differential operator that appears in the theory of minimal surfaces), the Hamilton–Jacobi equation (which is a formulation of classical mechanics that uses the principle of least action), the Jacobi method (which is an iterative algorithm for solving systems of linear equations), and the Jacobi eigenvalue algorithm (which is an iterative algorithm for computing the eigenvalues and eigenvectors of a real symmetric matrix). He also popularized the use of the symbol ∂ for partial derivatives¹. Jacobi suffered from poor health throughout his life and had to endure several periods of illness that interrupted his work. He contracted smallpox during the epidemic of 1850–1851 and died on 18 February 1851 in Berlin at the age of 46. He was buried at Trinity Cemetery in Berlin. His collected works were published in seven volumes by the Prussian Academy of Sciences between 1881 and 1891¹.