He taught himself mathematics: Who is Carl Gustav Jacob Jacobi?

Carl Gustav Jacob Jacobi (born 10 December 1804 in Potsdam – died 18 February 1851 in Berlin) was a German mathematician.

Carl Jacobi's first teacher was his uncle, who taught him mathematics and the classics and prepared him for the Potsdam Gymnasium. In 1816 he entered the aforementioned school. When he entered the University of Berlin in 1821, as the rector said, Jacobi had a universal intelligence. He might have been famous in philology, like Gauss, had he not been attracted to mathematics in the beginning. His teacher, Heinrich Bauer, left him to study alone, after many disagreements. Because Jacobi did not want to learn mathematics under certain rules and procedures.

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. His name is occasionally written as Carolus Gustavus Iacobus Iacobi in his Latin books, and his first name is sometimes given as Karl.

Young Jacobi's mathematical upbringing is similar to that of his greatest rival, Abel. He also applied to famous mathematicians like Abel. He learned algebra, integral and number theory from the works of Euler and Lagrange. He learned mathematics almost on his own and immediately established the theory of elliptic functions. The first mathematician to come after Euler in this field was Jacobi. Except for Ramanujan, the 19th-century Indian mathematician, Euler and Jacobi are no match for the most complicated algebraic calculations to come up with easily. Both Euler and Jacobi have been called algorithmists for this reason. Abel could easily use formulas if he wanted to. However, his genius was more philosophical and less oriented towards form than Jacobi's. Abel's fondness for mathematical accuracy is more like Gauss than Jacobi. This statement does not mean that there is a mistake in Jacobi's mathematics.

Not knowing that Abel was dealing with the general equation of the fifth degree in 1820, Jacobi tried to solve the same equation. By transforming this equation into x5-10·q2·x=p, he showed that its solution depends on solving a tenth-order equation. Although this solution didn't work well, it was a lesson in algebra for Jacobi. But, like Abel, he could not see that the general equation of the fifth degree cannot be solved. That's the difference between Abel and Jacobi and other mathematicians.

Jacobi was the first to apply elliptic functions to number theory. Thus, he easily solved one of Fermat's problems. In Jacobi, Lagrange, and Hamilton mechanics, the Hamilton – Jacobi equation is remembered. In particular, the advances made by Jacobi in differential equations are very important. His important scientific discoveries, such as Newton - Laplace - Lagrange theory of attraction, about the functions mentioned here, and his important scientific discoveries, such as the retraction of ellipsoids into operations of elliptic functions and especially Abelian functions, are above all praise. Jacobi's discovery of Abelian functions is more original and larger. They are derived from the inverse of Abelian integrals, just as elliptic functions are derived from the inverse of elliptic integrals.