内容简介 · · · · · ·
黎曼（18261866）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年后的今日，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。
《黎曼的学术遗产：150年巡礼（英文版）》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《黎曼的学术遗产：150年巡礼（英文版）》中，讨论了若干历史细节，并且着重介绍了黎曼所开创的数学领域的现代发展。
《黎曼的学术遗产：150年巡礼（英文版）》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。
目录 · · · · · ·
Riemann's Influence iGeometry， Analysis and Number Theory
Riemanns Saddlepoint Method and the RiemannSiegel Formula
The Period Matrices and Theta Functions of Riemann
Riemann's Hypothesis
Extensioof Holomorphic Functions Defined oNoReduced
· · · · · · (更多)
Riemann's Influence iGeometry， Analysis and Number Theory
Riemanns Saddlepoint Method and the RiemannSiegel Formula
The Period Matrices and Theta Functions of Riemann
Riemann's Hypothesis
Extensioof Holomorphic Functions Defined oNoReduced
Analytic Subvarieties
Bundles with Extra Geometric or Dynamic Structure
The Theory of Shock Waves： From Riemanthrough Today
Riemann's Existence Theorem
The Historical Roots of the Concept of RiemanSurfaces
The Story of Riemann's Moduli Space
Riemanand the ModerConcept of Space
Survey oAnalytic and Topological Torsion
The RiemanMinimal Examples
Manifolds of Mappings and Shapes
The RiemanHypothesis over Finite Fields： From Weil to the Present Day
The RiemannHurwitz Formula
Early History of the RiemanHypothesis iPositive Characteristic
Riemann's Influence iNumber Theory from a Computational and Experimental Perspective
RiemanProblem and Shock Capturing Schemes
A Discourse othe Measurable RiemanMapping Theorem &
Incompressible Fluid Motion
The Mertens Conjecture
Hodge Structures， Coniveau and Algebraic Cycles
· · · · · · (收起)
短评 · · · · · ·
黎曼的学术遗产:150年巡礼的话题 · · · · · · ( 全部 条 )
黎曼的学术遗产:150年巡礼的书评 · · · · · · ( 全部 0 条 )

3 What is good and great mathematics Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details...
20180309 10:36
3 What is good and great mathematics Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.(16) Birds and Frogs, Dyson #没想到数学家也能写出这么优美的句子，数学家很善于追求美好事物。
回应 20180309 10:36 
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts ...
20180307 19:20
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts and discouragements are part of life. Great mathematicians have doubts and get discouraged, but usually they can't stop doing mathematics anyway, and, when they do, they miss it very deeply.(16) Paul Halmos, HungarianJewishbornAmerican mathematician.
回应 20180307 19:20 
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to ...
20171122 20:06
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to describe the prospects of future progress, they did not limit themselves to the prospects of their own work. Today it seems that there are very few people with such an overview. This may be because we reward the specialist and not the person with the overview….(10) ——Mac Lane《The health of mathematics》 #大意指数学存在太多具体描述，不能够进行综述。
回应 20171122 20:06

Most mathematicians, but particularly those of the 'pure' variety, far removed from applications, have a clear idea of what is meant by a 'beautiful argument' . This is a term of great praise indicating elegance of style, economy of effort, clarity of thought, perfection of detail and balance of form adding up to give a feeling of overwhelming conviction. (1回应)
20171121 13:46
Most mathematicians, but particularly those of the 'pure' variety, far removed from applications, have a clear idea of what is meant by a 'beautiful argument' .
This is a term of great praise indicating elegance of style, economy of effort, clarity of thought, perfection of detail and balance of form adding up to give a feeling of overwhelming conviction.
1回应 20171121 13:46 
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to ...
20171122 20:06
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to describe the prospects of future progress, they did not limit themselves to the prospects of their own work. Today it seems that there are very few people with such an overview. This may be because we reward the specialist and not the person with the overview….(10) ——Mac Lane《The health of mathematics》 #大意指数学存在太多具体描述，不能够进行综述。
回应 20171122 20:06 
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts ...
20180307 19:20
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts and discouragements are part of life. Great mathematicians have doubts and get discouraged, but usually they can't stop doing mathematics anyway, and, when they do, they miss it very deeply.(16) Paul Halmos, HungarianJewishbornAmerican mathematician.
回应 20180307 19:20

3 What is good and great mathematics Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details...
20180309 10:36
3 What is good and great mathematics Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.(16) Birds and Frogs, Dyson #没想到数学家也能写出这么优美的句子，数学家很善于追求美好事物。
回应 20180309 10:36 
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts ...
20180307 19:20
What One Should Know About Riemann But May not Know? To be a mathematician you must love mathematics more than family, religion, money, comfort, pleasure, glory. I do not mean that you must love it to the exclusion of family, religion, and the rest, and I do not mean that if you do love it, you'll never be discouraged, you'll never be ready to chuck it all and take up gardening instead. Doubts and discouragements are part of life. Great mathematicians have doubts and get discouraged, but usually they can't stop doing mathematics anyway, and, when they do, they miss it very deeply.(16) Paul Halmos, HungarianJewishbornAmerican mathematician.
回应 20180307 19:20 
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to ...
20171122 20:06
Now in each of these illustrative examples of mathematics gone wild, the specialist may well see a purpose with eluded me. But I still contend that there are far too many such cases of elaboration without illumination, and that this is the price of persistent specialization…(10) In the past times there were at least some mathematicians who had a general overview of the whole subject; asked to describe the prospects of future progress, they did not limit themselves to the prospects of their own work. Today it seems that there are very few people with such an overview. This may be because we reward the specialist and not the person with the overview….(10) ——Mac Lane《The health of mathematics》 #大意指数学存在太多具体描述，不能够进行综述。
回应 20171122 20:06
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