Carl Gustav Jakob Jacobi (1804 - 1851) was born in Germany. His father was a prosperous banker, never missing anything. He obtained a good education at the University of Berlin, focusing on Philosophy and Mathematics to which he devoted himself entirely. He was a born teacher and liked to convey his ideas. At about the same time as Gauss and Abel, Jacobi developed the theory of elitic functions. Knowing that Abel had given Cauchy some articles on the subject, Jacobi wrote to the French master asking for them in the hope of obtaining information to confirm his discovery. Cauchy, however, had lost Abel's writings.
His classic treatise "Foundations of the New Theory of Elitic Functions" appeared in 1829, the year of Abel's death, and received praise even from Legendre. In 1834 it proved that if a univocal function of a variable is doubly periodic, the ratio between periods cannot be real and it is impossible for it to have more than two distinct periods. We also owe him the study of Jacobi's "theta functions," whole functions of which the elliptics are quotient.
Until that time, the theory of determinants appeared in the works of some mathematicians such as Leibniz, Cramer, and Lagrange, but with sporadic ideas. The continuous development of this theory took place only in the 11th century and its main collaborator was Jacobi, in addition to Cauchy, building algorithms, giving practical rules with great concern for determinant notations, and in 1829 first used the "Jacobians", special determinants. analogues for multi-variable functions, the differential quotient of a single-variable function. Through them, he was able to prove the Fermat-Lagrange four-square theorem and also by using the Jacobians he could know when a collection of functions is independent. Jacobi's articles, as well as those of Abel and Dirichlet appeared frequently in Crelle's Journal.
In 1842, when Jacobi visited Paris, he was asked who was the greatest living English mathematician, and he, struck by so many important French discoveries, replied, "There are none," which was considered very inelegant and cruel on his part.
Source: Fundamentals of Elementary Mathematics, Gelson Iezzi - Current Publisher