Bernhard Riemann (17/09/1826 – 20/07/1866)

Georg Friedrich Bernhard Riemann родился 17 сентября 1826 в Breselenz, Germany в семье пастора. Начальное образование получил в семье у отца. В школу пошёл 14 лет от роду. Боялся выступать перед аудиторией и любил решать головоломки. После окончания гимназии провёл год в Гёттингенском университете и уехал в Берлин, где учился у крупнейших математиков того времени (Якоби, Штайнер, Эйзенштейн). Вернулся в Göttingen in 1849 to finish his doctoral work. He submitted his thesis in 1851 to Gauss. It impressed Gauss, who said Riemann possessed a "Gloriously fertile originality." Riemann was later appointed to a post at Göttingen on Gauss's recommendation. During his time there, he wrote another thesis on mathematics. Published in 1854, it was called Über Hypothesen welche der Geometrie zu Grunde liegen, which means About the hypotheses which are the basis of Geometry. This paper eventually became a classic of mathematics. In fact, Albert Einstein used its results in his relativistic theory of gravitation. After Gauss died in 1855, Dirichlet took over his position at Göttingen. He was in turn succeeded by Riemann. Riemann was at this time suffering from tuberculosis. He spent his remaining time travling between Germany and Italy trying to get better. Riemann died there in Selasca, Italy on July 20, 1866.

Franz Mertens (20/03/1840 – 05/03/1927)

Franz Mertens was born into a partitioned Poland, the third of the three partitions took place in 1795 and split Poland between Russia, Prussia and Austria. Sroda, the village in which Mertens was born, was close to Poznan in Prussia. Mertens completed his university studies at the University of Berlin where he attended lectures by Weierstrass, Kronecker and Kummer. This was the "golden period" for mathematics in Berlin and gave Mertens the best possible mathematical foundations. In 1865 he obtained his doctorate with a dissertation De functione potentiali duarum ellipsoidium homogenearum. His advisors had been Kummer and Kronecker.

He worked first in the Jagiellonian University at Cracow, at this time part of the Austrian region of Poland, being appointed as an extraordinary professor in 1865, and then promoted to an ordinary professor in 1870. He was called to the Polytechnic in Graz in Austria in 1884 then, remaining in Austria, from 1894 he was an ordinary professor of mathematics at the University of Vienna. He retired in 1911 but, being made Professor Emeritus, he continued to give lectures. He supervised the doctoral theses of a number of excellent mathematicians while in Vienna. He also lectured to Schrödinger in mathematics at around the same time. Мертенс работал в нескольких областях, таких как теория потенциала, геометрические приложения детерминантов, алгебра и аналитическая теория чисел, опубликовав 126 работ.

1 Конспект подготовлен на основе учебника У.Рудина «Основы математического анализа». «Мир»,М., 1966