By Detlef Laugwitz
The identify of Bernard Riemann is celebrated to mathematicians and physicists around the globe. His identify is indelibly stamped at the literature of arithmetic and physics. This impressive paintings, wealthy in perception and scholarship, is addressed to mathematicians, physicists, and philosophers attracted to arithmetic. It seeks to attract these readers toward the underlying principles of Riemann’s paintings and to the improvement of them of their historic context. This illuminating English-language model of the unique German version might be a huge contribution to the literature of the historical past of mathematics.
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Additional resources for Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics (Modern Birkhäuser Classics)
1 1 zero. 1 Bernhard R i e m a n n in his time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . zero. 1. 1 His lifestyles and the improvement of his character . . . . . . . . . . . . . . . . . . . . . 1 zero. 1. 2 The political and e c o n o m i c scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . three zero. 1. three Upbringing and schooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . five zero. 1. four R i e m a n n ' s place of birth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . nine zero. 1. five G6ttingen and Berlin as facilities of analysis . . . . . . . . . . . . . . . . . . . . . . . . . 17 zero. 1. 6 R i e m a n n as complete professor: 1 eight five nine - 1 eight 6 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 zero. 2 The golden 1850s in G6ttingen: From Gauss and Dirichlet to R i e m a n n and Dedekind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 zero. 2. 1 R i e m a n n and Dedekind: own conditions . . . . . . . . . . . . . . . . . . 24 zero. 2. 2 in the direction of switch in arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 zero. 2. three Snapshots by way of an English observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 zero. three affects within the ultimate years" Riemann among G e r m a n y and Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 zero. four zero. four. 1 C o m p e t i n g conceptions of study earlier than Riemann . . . . . . . . . . . . . . forty three R i e m a n n within the old evolution of research" an summary . . . . . . forty three zero. four. 2 Algebraic research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . forty six zero. four. three Infinitesimal research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fifty two zero. four. four G e o m e t r i c deliberations: Fourier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fifty five zero. four. five The restrict perception: Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . fifty six zero. four. 6 in the direction of epsilontics: Cauchy and Dirichlet . . . . . . . . . . . . . . . . . . . . . . . fifty seven 1. advanced research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sixty four 1. 1 The genesis of complicated research as much as R i e m a n n ' s time . . . . . . . . . . . . sixty four 1. 1. 1 initial comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sixty four 1. 1. 2 The advanced numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . sixty five 1. 1. three complicated features and their derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . sixty nine 1. 1. four Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seventy three vi Contents 1. 1. five strength sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . seventy seven 1. 1. 6 extra purposes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eighty four 1. 1. 7 Multivalued services and R i e m a n n surfaces . . . . . . . . . . . . . . . . . . . . . 88 1. 1. eight D o u b l y periodic capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety two 1. 2 The dissertation of 1851 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety six 1. 2. 1 R i e m a n n ' s view of the causes for the paper: Article 20 1. 2. 2 a quick account of the contents of the dissertation . . . . . . . . . . . . . . . . 1. 2. three R i e m a n n ' s s u m m a r y of the dissertation. this system- of the dissertation, half I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety six ninety nine Article 20, and half II, Article 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . one zero one 1. 2. four at the prehistory of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 1. 2. five The impact of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 1. three The gildings . . . . . . .