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in Germany and France. Leaving Norway in 1825, Abel visited the astronomer, Schumacher, in Hamburg, and spent six months in Berlin, where he became intimate with August Leopold Crelle (1780–1855), and met Steiner. Encouraged by Abel and Steiner, Crelle started his journal in 1826. Abel began to put some of his work in shape for print. His proof of the impossibility of solving the general equation of the fifth degree by radicals,—first printed in 1824 in a very concise form, and difficult of apprehension,—was elaborated in greater detail, and published in the first volume. He entered also upon the subject of infinite series (particularly the binomial theorem, of which he gave in Crelle's Journal a rigid general investigation), the study of functions, and of the integral calculus. The obscurities everywhere encountered by him owing to the prevailing loose methods of analysis he endeavoured to clear up. For a short time he left Berlin for Freiberg, where he had fewer interruptions to work, and it was there that he made researches on hyperelliptic and Abelian functions. In July, 1826, Abel left Germany for Paris without having met Gauss! Abel had sent to Gauss his proof of 1824 of the impossibility of solving equations of the fifth degree, to which Gauss never paid any attention. This slight, and a haughtiness of spirit which he associated with Gauss, prevented the genial Abel from going to Göttingen. A similar feeling was entertained by him later against Cauchy. Abel remained ten months in Paris. He met there Dirichlet, Legendre, Cauchy, and others; but was little appreciated. He had already published several important memoirs in Crelle's Journal, but by the French this new periodical was as yet hardly known to exist, and Abel was too modest to speak of his own work. Pecuniary embarrassments induced him to return home after a second short stay in Berlin. At Christiania he for some time gave private lessons, and served