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Encyclopedia Britannica - Main :: RHY-RON |
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RIEMANN, GEORG FRIEDRICH BERNHARD (18261866) , German mathematician, was born on the 17th of September II 1826, at Breselenz, near Dannenberg in Hanover. His father, Friedrich Bernhard Riemann, came from Mecklenburg, had served in the war of freedom, and had finally settled as pastor in Quickborn. Here with his five brothers and sisters Riemann spent his boyhood and received, chiefly from his father, the elements of his education. He showed at an early age well-marked mathematical powers, and his progress was so rapid in arithmetic and geometry that he was soon beyond the guidance not only of his father but of schoolmaster Schulz, who assisted in the mathematical department of his training. In 184o he went to Hanover, where he attended the lyceum, and two years later he entered the Johanneum at Luneburg. The director, Schmalfuss, encouraged him in his mathematical studies by lending him books (among them Leonhard Euler's works and Adrien Marie Legendre's Theory of Numbers), which Riemann read, mastered and returned within a few days. In 1846 Riemann entered himself as a student of philology and theology in the university of Gottingen. This choice of a university career was dictated more by the natural desire of his father to see his son enter his own profession, and by the poverty of his family, than by his own preference. He attended lectures on the numerical solution of equations and on definite integrals by M. A. Stern, on terrestrial magnetism by Goldschmidt, and on the method of least squares by K. F. Gauss. It soon became evident that his mathematical studies, undertaken at first probably as a relaxation, were destined to be the chief
In 185o he returned to Gottingen and began to prepare,his doctor
In November 1851 he obtained his doctorate, the thesis being " Grundlagen fur eine allgemeine Theorie der Functionen einer veranderlichen complexen Grosse." This memoir excited the admiration of Gauss, and at once marked its author's rank as a mathematician. The fundamental method of research which Riemann employed has just been alluded to; the results will be best indicated in his own words: " The methods in use hitherto for treating functions of a complex variable always started from an expression for the function as its definition, whereby its value was given for every value of the argument ; by our investigation it has been shown that, in consequence of the general character of a function of a complex variable, in a definition of this sort one part of the determining conditions is a consequence of the rest, and the extent of the determining conditions has been reduced to what is necessary to effect the determination. This essentially simplifies the treatment of such functions. Hitherto, in order to prove the equality of two expressions for the same function, it was necessary to transform the one into the other, i.e. to show that both expressions agreed for every value of the variable; now it is sufficient to prove their agreement to a far less extent " [merely in certain critical points and at certain boundaries].The time between his promotion to the doctorate and his habilitation as Privatdozent was occupied by researches undertaken for his Habilitationsschrift, by " Naturphilosophie,"and by experimental work. The subject he had chosen for his Habilitationsschrift was the "Representation of a Function by Means of a Trigonometrical Series ," a subject which Dirichlet had made his own by a now well-known series of researches. It was fortunate, no doubt, for Riemann that he had the kind advice and encouragement of Dirichlet himself, who was then on a visit at Gottingen during the preparation of his essay; but the result was a memoir of such originality and refinement as showed that the pupil was fully the equal of the master. Of the customary three themes which he suggested for his trial lecture, that " On the Hypotheses which form the Foundation of Geometry" was chosen at the instance of Gauss, who was curious to hear what so young a man had to say on this difficult subject, on which he himself had in private speculated so profoundly (see GEOMETRY, NON-EUCLIDIAN).In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor. In this they were not successful; but a government stipend of 200 thalers was given him, and even this miserable pittance was of great importance, so straitened were his circumstances. But this small beginning of good fortune was embittered by the deaths of his father and his eldest sister, and by the breaking up of the home at Quick
doctor
Riemann's health had never been strong. Even in his boyhood he had shown symptoms of consumption, the disease that was working such havoc in his family; and now under the strain of work he broke down altogether, and had to retire to the Harz with his friends Ritter and R. Dedekind, where he gave himself up to excursions and " Naturphilosophie." After his return to Gottingen (November 1857) he was made extra- ordinary professor, and his salary raised to 300 thalers. As usual with him, misfortune followed close behind; for he lost in quick
Maggiore . Here his strength rapidly ebbed away, but his mental faculties remained brilliant to the last. On the 19th of July 1866 he was working at his last unfinished investigation on the mechanism of the ear. The day following he died. Few as were the years of work allotted to him, and few as are the printed pages covered by the record of his researches, his name is, and will remain, a household word among mathematicians. Most of his memoirs are masterpiecesfull of original
The collected works of Riemann were published by H. Weber, assisted by R. Dedekind (8vo, Leipzig
At the end of this volume there is a touching account of his life disparagingly of him. But his power was already beginning by the latter. - (G. CH.) to wane. His extravagant pretensions only served to excite End of Article: RIEMANN, GEORG FRIEDRICH BERNHARD (18261866) If you wish, you can link directly to this article.
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