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Carl JacobiGerman mathematician.
Date of Birth: 10.12.1804
Country:  Germany |
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Biography of Karl Jacobi
Karl Jacobi was a German mathematician born on December 10, 1804 in Potsdam. He received his education at the University of Berlin. From 1826 to 1844, he served as a professor of mathematics at the University of Königsberg, and later, after a brief period in Italy, he became a professor at the University of Berlin.
Contributions to Mathematics
Jacobi's first notable work, "New Foundations of the Theory of Elliptic Functions" (Fundamenta nova theoriae functionum ellipticarum), was published in 1829, in the same year Abel passed away. Jacobi's research in this area was driven by a captivating competition with Abel. He developed the theory of elliptic functions based on four theta functions, defined by infinite series. In 1832, while solving the problem of inverting hyperelliptic integrals, Jacobi discovered that this inversion was possible by using functions with more than one variable. This led to the development of the theory of Abelian functions with p variables, which became an important branch of 19th-century mathematics.
Jacobi is also known for his work in the field of functional determinants. His publication "On the Formation and Properties of Determinants" (De formatione et proprietatibus determinantium) in 1841 introduced the concept of the Jacobian determinant, a well-known functional determinant. Furthermore, Jacobi made significant contributions to the theory of partial differential equations and their application to solving certain problems in dynamics. His remarkable "Lectures on Dynamics" (Vorlesungen über Dynamik), published in 1866 based on notes from 1842-1843, includes an interesting chapter on the definition of geodesic lines on an ellipsoid. This problem led to a relationship between two Abelian integrals.
Legacy
Karl Jacobi passed away on February 18, 1851 in Berlin. His contributions to mathematics, particularly in the areas of elliptic functions, functional determinants, and differential equations, have left a lasting impact on the field. The Jacobian determinant, named in his honor, remains an important mathematical concept studied to this day.
