黎曼(1826—1866) 对数学有着独特的创造力和广博的洞察力，同时对数学的处理富有强有力的技巧和远见的思想。在他短暂的一生中，黎曼对数学几乎所有的分支都有着广泛的影响。时至150年的今日，我们仍然要尝试理解在数学后续发展中的黎曼的工作以及他的数学思想。
我们邀请了一批具有前沿思想的专家撰写了相关的综述和展望性质的文章，希望这些专题也会是黎曼所感兴趣的。
在本文集中，我们讨论了若干历史细节，并且着重介绍了在黎曼所开创的数学领域的现代发展。本书对于希望了解黎曼深邃的数学思想及其对现代数学影响的读者具有重要的参考价值。
- Front Matter
- What One Should Know About Riemann But May Not Know?
- Lizhen Ji, Shing-Tung Yau
- Riemann’s Influence in Geometry, Analysis and Number Theory
- Riemann’s Saddle-point Method and the Riemann-Siegel Formula.
- The Period Matrices and Theta Functions of Riemann
- Riemann’s Hypothesis
- Extension of Holomorphic Functions Defined on Non Reduced Analytic Subvarieties
- Bundles with Extra Geometric or Dynamic Structure
- The Theory of Shock Waves: From Riemann through Today
- James Glimm, Dan Marchesin, and Bradley Plohr
- Riemann’s Existence Theorem
- The Historical Roots of the Concept of Riemann Surfaces
- The Story of Riemann’s Moduli Space
- Riemann and the Modern Concept of Space .
- Survey on Analytic and Topological Torsion .
- The Riemann Minimal Examples
- William H. Meeks III, Joaqu´ın P´erez
- Manifolds of Mappings and Shapes
- The Riemann Hypothesis over Finite Fields: From Weil to the Present Day .
- The Riemann-Hurwitz Formula
- Early History of the Riemann Hypothesis in Positive Characteristic
- Frans Oort, Norbert Schappacher
- Riemann’s Influence in Number Theory from a Computational and Experimental Perspective
- Riemann Problem and Shock Capturing Schemes .
- A Discourse on the Measurable Riemann Mapping Theorem &Incompressible Fluid Motion
- The Mertens Conjecture
- Hodge Structures, Coniveau and Algebraic Cycles
