information:classification, structural:summarization
Back to Prussia, Breslau (1825–1828)

As General Foy died in November 1825 and he could not find any paying position in France, Dirichlet had to return to Prussia. Fourier and Poisson introduced him to Alexander von Humboldt, who had been called to join the court of King Friedrich Wilhelm III. Humboldt, planning to make Berlin a center of science and research, immediately offered his help to Dirichlet, sending letters in his favour to the Prussian government and to the Prussian Academy of Sciences. Humboldt also secured a recommendation letter from Gauss, who upon reading his memoir on Fermat's theorem wrote with an unusual amount of praise that "Dirichlet showed excellent talent". With the support of Humboldt and Gauss, Dirichlet was offered a teaching position at the University of Breslau. However, as he had not passed a doctoral dissertation, he submitted his memoir on the Fermat theorem as a thesis to the University of Bonn. Again his lack of fluency in Latin rendered him unable to hold the required public disputation of his thesis; after much discussion, the university decided to bypass the problem by awarding him an honorary doctorate in February 1827. Also, the Minister of Education granted him a dispensation for the Latin disputation required for the Habilitation. Dirichlet earned the Habilitation and lectured in the 1827–28 year as a Privatdozent at Breslau.

While in Breslau, Dirichlet continued his number-theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gauss's research. Alexander von Humboldt took advantage of these new results, which had also drawn enthusiastic praise from Friedrich Bessel, to arrange for him the desired transfer to Berlin. Given Dirichlet's young age (he was 23 years old at the time), Humboldt was able to get him only a trial position at the Prussian Military Academy in Berlin while remaining nominally employed by the University of Breslau. The probation was extended for three years until the position becoming definite in 1831.