Jacobi's early education was given by an uncle on his mother's side, and then, just before his twelfth birthday, Jacobi entered the Gymnasium in Potsdam. He had been well taught by his uncle and he had remarkable talents. In 1817, while still in his first year of schooling, he was put into the final year class. This meant that by the end of the academic year 1816-17, he was still only 12 years old yet he had reached the necessary standard to enter a university. The University of Berlin did not accept students below the age of 16, so Jacobi had to remain in the same class at the Gymnasium in Potsdam until the spring of 1821.
Of course, Jacobi pressed on with his academic studies despite remaining in the same class at school. He received the highest awards for Latin, Greek and history but it was the study of mathematics which he took furthest. By the time Jacobi left school he had read advanced mathematics texts such as Euler's "Introductio" in analysin infinitorum and had been doing research on his own. He was attempting to solve Quintic Equations by Radicals.
Jacobi entered the University of Berlin in 1821 still unsure which topic he would concentrate on. He attended courses in philosophy, classics and mathematics for two years before realising that he had to make a definite decision between these subjects. He chose mathematics, but this did not mean that he could attend high level courses in mathematics for at this time the standard of university education in mathematics in Germany was rather poor. As he had done at the Gymnasium, Jacobi had to study on his own reading the works of Lagrange[->0] and other leading mathematicians.
By the end of academic year 1823-24 Jacobi had passed the examinations necessary for him to be able to teach mathematics, Greek, and Latin in secondary schools. Of course, one might have expected him to have problems obtaining a teaching position since, as we noted at the beginning of this article, he was Jewish. His brilliance appears to have been sufficient to allow this hurdle to be overcome for, in 1825, he was offered a teaching post at the Joachimsthalsche Gymnasium, one of the leading schools in Berlin. He had submitted his doctoral dissertation to the University of Berlin even before he received the offer of the teaching post, and he was allowed to move quickly to work on his habilitation[->1] thesis.
Jacobi presented a paper concerning iterated functions to the Berlin Academy of Sciences[->2] in 1825. However, the referees did not consider the results worth publishing and indeed the paper was not published by the Berlin Academy[->3]. The paper was published eventually, for in 1961 it was published with a commentary in [6[->4]]. Biermann, the author of [6[->5]], quotes the opinions of the original referees and criticises them strongly. Although this was not the best start for the young Jacobi, it did not hold him back for long and his publication record over the following years would be quite remarkable for both the number and quality of the works.
Around 1825 Jacobi changed from the Jewish faith to become a Christian which now made university teaching possible for him. By the academic year 1825-26 he was teaching at the University of Berlin. However prospects in Berlin were not good so, after taking advice from colleagues, Jacobi moved to the University of Königsberg arriving there in May 1826. There he joined Franz Neumann[->6], who had also received his doctorate from Berlin in 1825, and Bessel[->7] who was the professor of…