作者:
Morris Kline
出版社: Oxford University Press
出版年: 19641231
页数: 512
定价: USD 34.95
装帧: Paperback
ISBN: 9780195007145
出版社: Oxford University Press
出版年: 19641231
页数: 512
定价: USD 34.95
装帧: Paperback
ISBN: 9780195007145
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Mathematics in Western Culture的书评 · · · · · · ( 全部 17 条 )
西方文化史和数学原理的完美结合
记得去年暑假实习的时候有朋友推荐我学习数学的好方法就是从历史看起 5.5到复旦逛街的时候发现了这本书 就把它买了下来 一开始怕书翻译的不好 毕竟翻译的好的书实在太少了 但是读起来发现趣味无穷 可读性好强 完了之后 是我读过的书当中为数不多的不会累的书 数学知识和文化历...
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重新爱上数学，从本书开始
这篇书评可能有关键情节透露
首先，在读《什么是数学？》一书前，读读《西方文化中的数学》比较好，因为读书要讲究循序渐进，后者是更为低阶的。 其次内容上，本书构造了以数学为中心的宏观地图，按时间顺序讲述，方便读者明白数学如何发展到今日（1953年），以及数学存在的意义。 再是形式上，作者克莱因... (展开)数学从生活中引发的思考
本书从反复实验法、类比法、归纳法以及演绎法入手对数学的基础进行了描述，再而描述了研究过程的方法论以及代表人物的研究思想以及方法。最后将数学与物理相结合，阐释数学。 数学本身是一为现实世界服务的，玩数学游戏的人会认为这是一门艺术。而作为一名物理学爱...
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年代较早，但依然精彩
这本书的年代较早，现在的数学对文化的影响就更大了。不过有两个观点让我感触还是很深的：1、理性的力量在数学发展史中的作用，希腊人的理性和罗马人的实用主义形成了鲜明对比；2、很多数学内容并不是出于实际的需求产生的，纯数学的研究也是有很大意义的。
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淇厚生 (士为悦己者读书)
pvii Almost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and ...20141028 19:39
pviiAlmost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and rebuilt religious doctrines, has supplied substance to economics and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe. As the embodiment and most powerful advocate of the rational spirit, mathematics had invaded domains ruled by authority, custom, and habit, and supplanted them as the arbiter of thought and action. Finally, as an incomparably fine human achievement mathematics offers saticfactions and aesthetic values at least equal to those offered by any other branch of our culture. 按：按Hardy的观点，这种说法夸大了数学的重要和影响，见《自白》27节。School courses and books have presented 'mathematics' as a series of apparently meaningless technical procedures. Such material is as representative of the subject as an account of the name, position, and function of every bone in the human skeleton is representative of the living, thinking, and emotional being called man.pixConfidence in man's power to solve his problems and indications of the method he has employed most successfully thus far can be gained by a study of his greatest and most enduring intellectual accomplishmentmathematics.p4The subject is not a series of techniques. These are indeed the least important aspect, and they fall as far short of representing mathematics as color mixing does of painting.To describe mathematics as only a method of inquiry iss to describe da Vinci's 'Last Supper' as an organization of paint on canvas. Mathematics is, also, a field for creative endeavor. In divining what can be proved, as well as in constructing methods of proof, mathematicians employ a high order of intuition and imagination.p5If mathematics is indeed a creative activity, what driving force causes men to pursue it. The most obvious, though not necessarily the most important, motive for mathematical investigations has been to answer questions arising directly out of social needs.Another basic use of mathematics, indeed one that is especially prominent in modern times, has been to provide a rational organization of natural phenomena.Intellectual curiosity and zest for pure thought have started many mathematicians in pursuit of properties of numbers and geometric figures and have produced some of the most original contributions.Over and above all other drives to create is the search for beauty.p6In addition to the beauty of the completed structure, the indispensable use of imagination and intuition in the creation of proofs and conclusions affords high aesthetic satisfaction to the creator.Despite the clear indications of history that all of the factors above have motivated the creation of mathematics there have been many erroneous pronouncements. There are the chargesoften made to excuse neglect of the subjectthat mathematicians like to indulge in pointless speculations or that they are silly and useless dreamers. To these charges a crushing reply can readily be made. Even purely abstract studies, let alone those motivated by scientific and engineering needs, have proved immensely useful. 按：将Kline的回应与他的另一段话对比。Morris Kline, Mathematics: The Loss of Certainty, Oxford University Press, p285: Some pure mathematicians argue that there is potential usefulness in any mathematical development and no one can foresee its actual future application. Nevertheless, a mathematical theme is like a piece of oilbearing land. Dark puddles on the surface may suggest that a particular spot be explored for oil and, if this is discovered, the value of the land is established. The proven worth of the land warrants further drilling in the expectation that more oil will be found if the drilling sites are not too far removed from the location of the original strike. Of course, one might choose a very distant site because the drilling is easier there and still claim that he will strike oil. But human effort and ingenuity are limited and should therefore be devoted to good risks.对于MLC这段话表达的观点，Timothy Gowers的演讲The Importance of Mathematics中有一个非常好的反驳。p7Practical, scientific, aesthetic, and philosophical interests have all shaped mathematics. It would be impossible to separate the contributions and influences of any one of these forces and weigh it against the others, much less assert sweeping claims to its relative importance.p8Mathematical language is precise, so precise that it is often confusing to people unaccustomed to its forms....This precision of mathematics appears as pedantry or stiltedness to one who does not yet appreciate that it is essential to exact thinking, for exact thinking and exact language go hand in hand.Mathematical style aims at brevity formal perfection. It sometimes succeeds two well and sacrifices the clarity its precision seeks to guarantee.p9Mathematics is more than a method, an art, and a language. It is a body of language with content that serves the physical and social scientist, the philosopher, the logician, and the artist; content that influences the doctrines of statesman and theologians; content that sacrifices the curiosity of the man who surveys the heavens and the man who muses on the sweetness of musical sounds; and content that has undeniably, if sometimes imperceptibly, shaped the course of modern history.p10In its broadest aspect mathematics is a spirit, the spirit of rationality. It is this spirit that challenges, stimulates, invigorates, and drives human minds to exercise themselves to the fullnest. p11This sketch of the life of mathematics, however brief, may nevertheless indicate that its vitality has been very much depentent on the cultural life of the civilazation which nourished it. In fact, mathematics has been so much a part of civilizations and cultures that many historians see mirrored in the mathematics of an age the characteristics of the other chief works of that age.It is also true that the absense of mathematics creations is indicative of the culture of a civilization.p178The difficulty most people experience in accepting a fourdimensional geometry and the corresponding equations is due to fact that they confuse mental constructions and visualization. All of geometry, including two and threedimensional Euclidean geometry, deals, as Plato emphasized, with ideas that exist in the mind only. Fortunately we can visualize or picture the two and threedimensional ideas by means of drawings on paper, and these drawings help us to remember and to organize our thoughts. But the pictures are not the subject matter of geometry and we are not permitted to reason from them.按：Timothy Gowers, Mathematics VSI, Oxford University Press, p77: Although visualizing an object feels rather like looking at it, there are important differences between the two experiences. For example, if I am asked to visualize a room with which I am familiar, but not very familiar, I have no difficulty in doing so. If I am then asked simple questions about it, such as how many chairs it contains or what colour the floor is, I am often unable to answer them. This shows that, whatever a mental image is, it is not a photographic representation.p206The major values of the Newtonian laws lies, as we have just seen, in the fact that they apply to so many varied situations on heaven and Earth.p232It was a very fortunate circumstence that mathematics and science were closely linked in the Newtonian era and that physical reasoning could guide the mathematician and keep them on the right track.p258Newton, along with Descartes, credited God with the act of creation but restricted His daily functions.p278Dryden declared: 'A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure, a mathematical head to be a complete and excellent poet...'p279The principles of form in poetry were likened to mathematical axioms because the axioms determined the form as well as the content of the theorems.p367Mathematics begins after the probabilities are known and is concerned with reasoning about the numbers so obtained.p379yet physicists believe that each molecure follows the same physical laws that the earth follows in its path around the sun....,but that these procedures are too intricate to be grasped by our understandings. The same could be said of economic phenomena, the incidence of death, and other seemingly unlawful affairs. Thus phenomena that appear to be disorderly may be completely determined, and the mathematical laws obtained from statistical studies may merely reflect the existence of these underlying orderly physical processes.按：The dialogue in XXIV is very interesting and inspiring.p459The description of mathematics as tautology says that the choice of a set of axioms is like the purchase of a piece of mining landthe riches are all there. This description omits, however, the patient, hard digging which must be performed, the careful sifting of the precious metal from the base rock, the value and beauty of the treasure obtained, and the pleasure and exhilaration of accomplishment.回应 20141028 19:39

淇厚生 (士为悦己者读书)
pvii Almost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and ...20141028 19:39
pviiAlmost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and rebuilt religious doctrines, has supplied substance to economics and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe. As the embodiment and most powerful advocate of the rational spirit, mathematics had invaded domains ruled by authority, custom, and habit, and supplanted them as the arbiter of thought and action. Finally, as an incomparably fine human achievement mathematics offers saticfactions and aesthetic values at least equal to those offered by any other branch of our culture. 按：按Hardy的观点，这种说法夸大了数学的重要和影响，见《自白》27节。School courses and books have presented 'mathematics' as a series of apparently meaningless technical procedures. Such material is as representative of the subject as an account of the name, position, and function of every bone in the human skeleton is representative of the living, thinking, and emotional being called man.pixConfidence in man's power to solve his problems and indications of the method he has employed most successfully thus far can be gained by a study of his greatest and most enduring intellectual accomplishmentmathematics.p4The subject is not a series of techniques. These are indeed the least important aspect, and they fall as far short of representing mathematics as color mixing does of painting.To describe mathematics as only a method of inquiry iss to describe da Vinci's 'Last Supper' as an organization of paint on canvas. Mathematics is, also, a field for creative endeavor. In divining what can be proved, as well as in constructing methods of proof, mathematicians employ a high order of intuition and imagination.p5If mathematics is indeed a creative activity, what driving force causes men to pursue it. The most obvious, though not necessarily the most important, motive for mathematical investigations has been to answer questions arising directly out of social needs.Another basic use of mathematics, indeed one that is especially prominent in modern times, has been to provide a rational organization of natural phenomena.Intellectual curiosity and zest for pure thought have started many mathematicians in pursuit of properties of numbers and geometric figures and have produced some of the most original contributions.Over and above all other drives to create is the search for beauty.p6In addition to the beauty of the completed structure, the indispensable use of imagination and intuition in the creation of proofs and conclusions affords high aesthetic satisfaction to the creator.Despite the clear indications of history that all of the factors above have motivated the creation of mathematics there have been many erroneous pronouncements. There are the chargesoften made to excuse neglect of the subjectthat mathematicians like to indulge in pointless speculations or that they are silly and useless dreamers. To these charges a crushing reply can readily be made. Even purely abstract studies, let alone those motivated by scientific and engineering needs, have proved immensely useful. 按：将Kline的回应与他的另一段话对比。Morris Kline, Mathematics: The Loss of Certainty, Oxford University Press, p285: Some pure mathematicians argue that there is potential usefulness in any mathematical development and no one can foresee its actual future application. Nevertheless, a mathematical theme is like a piece of oilbearing land. Dark puddles on the surface may suggest that a particular spot be explored for oil and, if this is discovered, the value of the land is established. The proven worth of the land warrants further drilling in the expectation that more oil will be found if the drilling sites are not too far removed from the location of the original strike. Of course, one might choose a very distant site because the drilling is easier there and still claim that he will strike oil. But human effort and ingenuity are limited and should therefore be devoted to good risks.对于MLC这段话表达的观点，Timothy Gowers的演讲The Importance of Mathematics中有一个非常好的反驳。p7Practical, scientific, aesthetic, and philosophical interests have all shaped mathematics. It would be impossible to separate the contributions and influences of any one of these forces and weigh it against the others, much less assert sweeping claims to its relative importance.p8Mathematical language is precise, so precise that it is often confusing to people unaccustomed to its forms....This precision of mathematics appears as pedantry or stiltedness to one who does not yet appreciate that it is essential to exact thinking, for exact thinking and exact language go hand in hand.Mathematical style aims at brevity formal perfection. It sometimes succeeds two well and sacrifices the clarity its precision seeks to guarantee.p9Mathematics is more than a method, an art, and a language. It is a body of language with content that serves the physical and social scientist, the philosopher, the logician, and the artist; content that influences the doctrines of statesman and theologians; content that sacrifices the curiosity of the man who surveys the heavens and the man who muses on the sweetness of musical sounds; and content that has undeniably, if sometimes imperceptibly, shaped the course of modern history.p10In its broadest aspect mathematics is a spirit, the spirit of rationality. It is this spirit that challenges, stimulates, invigorates, and drives human minds to exercise themselves to the fullnest. p11This sketch of the life of mathematics, however brief, may nevertheless indicate that its vitality has been very much depentent on the cultural life of the civilazation which nourished it. In fact, mathematics has been so much a part of civilizations and cultures that many historians see mirrored in the mathematics of an age the characteristics of the other chief works of that age.It is also true that the absense of mathematics creations is indicative of the culture of a civilization.p178The difficulty most people experience in accepting a fourdimensional geometry and the corresponding equations is due to fact that they confuse mental constructions and visualization. All of geometry, including two and threedimensional Euclidean geometry, deals, as Plato emphasized, with ideas that exist in the mind only. Fortunately we can visualize or picture the two and threedimensional ideas by means of drawings on paper, and these drawings help us to remember and to organize our thoughts. But the pictures are not the subject matter of geometry and we are not permitted to reason from them.按：Timothy Gowers, Mathematics VSI, Oxford University Press, p77: Although visualizing an object feels rather like looking at it, there are important differences between the two experiences. For example, if I am asked to visualize a room with which I am familiar, but not very familiar, I have no difficulty in doing so. If I am then asked simple questions about it, such as how many chairs it contains or what colour the floor is, I am often unable to answer them. This shows that, whatever a mental image is, it is not a photographic representation.p206The major values of the Newtonian laws lies, as we have just seen, in the fact that they apply to so many varied situations on heaven and Earth.p232It was a very fortunate circumstence that mathematics and science were closely linked in the Newtonian era and that physical reasoning could guide the mathematician and keep them on the right track.p258Newton, along with Descartes, credited God with the act of creation but restricted His daily functions.p278Dryden declared: 'A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure, a mathematical head to be a complete and excellent poet...'p279The principles of form in poetry were likened to mathematical axioms because the axioms determined the form as well as the content of the theorems.p367Mathematics begins after the probabilities are known and is concerned with reasoning about the numbers so obtained.p379yet physicists believe that each molecure follows the same physical laws that the earth follows in its path around the sun....,but that these procedures are too intricate to be grasped by our understandings. The same could be said of economic phenomena, the incidence of death, and other seemingly unlawful affairs. Thus phenomena that appear to be disorderly may be completely determined, and the mathematical laws obtained from statistical studies may merely reflect the existence of these underlying orderly physical processes.按：The dialogue in XXIV is very interesting and inspiring.p459The description of mathematics as tautology says that the choice of a set of axioms is like the purchase of a piece of mining landthe riches are all there. This description omits, however, the patient, hard digging which must be performed, the careful sifting of the precious metal from the base rock, the value and beauty of the treasure obtained, and the pleasure and exhilaration of accomplishment.回应 20141028 19:39

淇厚生 (士为悦己者读书)
pvii Almost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and ...20141028 19:39
pviiAlmost everyone knows that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and rebuilt religious doctrines, has supplied substance to economics and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe. As the embodiment and most powerful advocate of the rational spirit, mathematics had invaded domains ruled by authority, custom, and habit, and supplanted them as the arbiter of thought and action. Finally, as an incomparably fine human achievement mathematics offers saticfactions and aesthetic values at least equal to those offered by any other branch of our culture. 按：按Hardy的观点，这种说法夸大了数学的重要和影响，见《自白》27节。School courses and books have presented 'mathematics' as a series of apparently meaningless technical procedures. Such material is as representative of the subject as an account of the name, position, and function of every bone in the human skeleton is representative of the living, thinking, and emotional being called man.pixConfidence in man's power to solve his problems and indications of the method he has employed most successfully thus far can be gained by a study of his greatest and most enduring intellectual accomplishmentmathematics.p4The subject is not a series of techniques. These are indeed the least important aspect, and they fall as far short of representing mathematics as color mixing does of painting.To describe mathematics as only a method of inquiry iss to describe da Vinci's 'Last Supper' as an organization of paint on canvas. Mathematics is, also, a field for creative endeavor. In divining what can be proved, as well as in constructing methods of proof, mathematicians employ a high order of intuition and imagination.p5If mathematics is indeed a creative activity, what driving force causes men to pursue it. The most obvious, though not necessarily the most important, motive for mathematical investigations has been to answer questions arising directly out of social needs.Another basic use of mathematics, indeed one that is especially prominent in modern times, has been to provide a rational organization of natural phenomena.Intellectual curiosity and zest for pure thought have started many mathematicians in pursuit of properties of numbers and geometric figures and have produced some of the most original contributions.Over and above all other drives to create is the search for beauty.p6In addition to the beauty of the completed structure, the indispensable use of imagination and intuition in the creation of proofs and conclusions affords high aesthetic satisfaction to the creator.Despite the clear indications of history that all of the factors above have motivated the creation of mathematics there have been many erroneous pronouncements. There are the chargesoften made to excuse neglect of the subjectthat mathematicians like to indulge in pointless speculations or that they are silly and useless dreamers. To these charges a crushing reply can readily be made. Even purely abstract studies, let alone those motivated by scientific and engineering needs, have proved immensely useful. 按：将Kline的回应与他的另一段话对比。Morris Kline, Mathematics: The Loss of Certainty, Oxford University Press, p285: Some pure mathematicians argue that there is potential usefulness in any mathematical development and no one can foresee its actual future application. Nevertheless, a mathematical theme is like a piece of oilbearing land. Dark puddles on the surface may suggest that a particular spot be explored for oil and, if this is discovered, the value of the land is established. The proven worth of the land warrants further drilling in the expectation that more oil will be found if the drilling sites are not too far removed from the location of the original strike. Of course, one might choose a very distant site because the drilling is easier there and still claim that he will strike oil. But human effort and ingenuity are limited and should therefore be devoted to good risks.对于MLC这段话表达的观点，Timothy Gowers的演讲The Importance of Mathematics中有一个非常好的反驳。p7Practical, scientific, aesthetic, and philosophical interests have all shaped mathematics. It would be impossible to separate the contributions and influences of any one of these forces and weigh it against the others, much less assert sweeping claims to its relative importance.p8Mathematical language is precise, so precise that it is often confusing to people unaccustomed to its forms....This precision of mathematics appears as pedantry or stiltedness to one who does not yet appreciate that it is essential to exact thinking, for exact thinking and exact language go hand in hand.Mathematical style aims at brevity formal perfection. It sometimes succeeds two well and sacrifices the clarity its precision seeks to guarantee.p9Mathematics is more than a method, an art, and a language. It is a body of language with content that serves the physical and social scientist, the philosopher, the logician, and the artist; content that influences the doctrines of statesman and theologians; content that sacrifices the curiosity of the man who surveys the heavens and the man who muses on the sweetness of musical sounds; and content that has undeniably, if sometimes imperceptibly, shaped the course of modern history.p10In its broadest aspect mathematics is a spirit, the spirit of rationality. It is this spirit that challenges, stimulates, invigorates, and drives human minds to exercise themselves to the fullnest. p11This sketch of the life of mathematics, however brief, may nevertheless indicate that its vitality has been very much depentent on the cultural life of the civilazation which nourished it. In fact, mathematics has been so much a part of civilizations and cultures that many historians see mirrored in the mathematics of an age the characteristics of the other chief works of that age.It is also true that the absense of mathematics creations is indicative of the culture of a civilization.p178The difficulty most people experience in accepting a fourdimensional geometry and the corresponding equations is due to fact that they confuse mental constructions and visualization. All of geometry, including two and threedimensional Euclidean geometry, deals, as Plato emphasized, with ideas that exist in the mind only. Fortunately we can visualize or picture the two and threedimensional ideas by means of drawings on paper, and these drawings help us to remember and to organize our thoughts. But the pictures are not the subject matter of geometry and we are not permitted to reason from them.按：Timothy Gowers, Mathematics VSI, Oxford University Press, p77: Although visualizing an object feels rather like looking at it, there are important differences between the two experiences. For example, if I am asked to visualize a room with which I am familiar, but not very familiar, I have no difficulty in doing so. If I am then asked simple questions about it, such as how many chairs it contains or what colour the floor is, I am often unable to answer them. This shows that, whatever a mental image is, it is not a photographic representation.p206The major values of the Newtonian laws lies, as we have just seen, in the fact that they apply to so many varied situations on heaven and Earth.p232It was a very fortunate circumstence that mathematics and science were closely linked in the Newtonian era and that physical reasoning could guide the mathematician and keep them on the right track.p258Newton, along with Descartes, credited God with the act of creation but restricted His daily functions.p278Dryden declared: 'A man should be learned in several sciences, and should have a reasonable, philosophical and in some measure, a mathematical head to be a complete and excellent poet...'p279The principles of form in poetry were likened to mathematical axioms because the axioms determined the form as well as the content of the theorems.p367Mathematics begins after the probabilities are known and is concerned with reasoning about the numbers so obtained.p379yet physicists believe that each molecure follows the same physical laws that the earth follows in its path around the sun....,but that these procedures are too intricate to be grasped by our understandings. The same could be said of economic phenomena, the incidence of death, and other seemingly unlawful affairs. Thus phenomena that appear to be disorderly may be completely determined, and the mathematical laws obtained from statistical studies may merely reflect the existence of these underlying orderly physical processes.按：The dialogue in XXIV is very interesting and inspiring.p459The description of mathematics as tautology says that the choice of a set of axioms is like the purchase of a piece of mining landthe riches are all there. This description omits, however, the patient, hard digging which must be performed, the careful sifting of the precious metal from the base rock, the value and beauty of the treasure obtained, and the pleasure and exhilaration of accomplishment.回应 20141028 19:39
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